Gallery #3 seems to do this (going straight to the thumbnail page without a Splash Page).

On my iPod Touch, Gallery #3 displays in Small Screen Mode (not Large Screen Mode). Only Small Screen Mode displays the thumbnails and main images on different pages. (Large Screen Mode would display the thumbnails and images on the same page.)

Try scaling your web page for mobile devices by using the following <meta> 'viewport' tag in the <head> section of your page (rather than the one you currently use):

<meta name="viewport" content="width=device-width, initial-scale=1">

Juicebox takes into account the device itself as well as the screen size when deciding which Screen Mode to use. It is not possible to change the internal logic which determines the Screen Mode but you can force a certain Screen Mode to be used via the screenMode configuration option (although I understand that you do not want to do this).

Apple removed 'minimal-ui' from iOS 8 (which was used to remove the bars from the screen in previous versions of iOS).
Your web page still includes 'minimal-ui' (in the <meta> 'viewport' tag) which is why the bars still disappear on devices running versions of IOS prior to 8 (but not on the iPhone 6 Plus which I expect is running iOS 8).

This is entirely up to the author of the gallery to decide and might be somewhat dependent on the target audience for your web site. For example, if it is highly likely that visitors to your web site will be viewing your web pages on large desktop monitors (rather than small mobile devices), then you could perhaps get away with not having to provide small images in your galleries.

Incidentally, as you switch between galleries using links in a header, you might like to take a look at the Using a Resizable Gallery with a Header support section.
The View Resizable Gallery with Top Menu Example uses a header with links to different galleries (like your web pages do) and the remainder of the browser window space is used for the galleries without the need for any vertical scroll bars (which your web pages currently use).
You could view the source of the demo web pages in a browser and copy/modify them to suit your own needs.

JuiceboxBuilder-Pro and the Juicebox-Pro Lightroom plugin are similar in that they both have individual controls for all Pro configuration options and they both have a live preview window which displays the gallery as the options are being changed.
However, JuiceboxBuilder-Pro has some additional features that are not found in any plugin.
JuiceboxBuilder-Pro has the ability to open and edit an existing gallery (whether it was created with JuiceboxBuilder-Pro or the Lightroom plugin).
Also, JuiceboxBuilder-Pro has Multi-Size Image Support. (The Lightroom plugin is unable to export multiple different sizes of images at once so does not feature this functionality.)
It is also easier to input custom image titles and captions using JuiceboxBuilder-Pro (on the 'Images' tab) but the Lightroom plugin allows the extraction of more EXIF and IPTC metadata fields (for use as titles and captions) than JuiceboxBuilder-Pro does.
There may be a few other subtle differences but these are the main points.

More information about JuiceboxBuilder can be found in the following links:
JuiceboxBuilder Tour: http://www.juicebox.net/tour/juiceboxbuilder/
JuiceboxBuilder User Guide: http://www.juicebox.net/support/juiceboxbuilder/

The Lightroom plugin's support page can be found here:
Lightroom Plugin: http://www.juicebox.net/support/lightroom/

Please post the URL to your gallery so that I can take a look and help further.
Thank you.

(Also, please make sure that your gallery does not set screenMode="LARGE" which would force the gallery to be displayed in Large Screen Mode on all devices and in all browsers.)

What you are describing sounds like the Splash Page.
The Splash Page is a placeholder for the gallery which is displayed by default on small screen devices when the gallery is embedded in a page alongside other content (rather than displayed on a page of its own with dimensions of 100% x 100%, filling the browser window).
When the user taps the Splash Page, the gallery is expanded to fill the user's browser window.
For more information about the Splash Page and how Juicebox adapts to different devices and screen sizes, please see here.

You can choose to not use the Splash Page by setting showSplashPage="NEVER" (in JuiceboxBuilder-Pro's 'Customize -> Splash Page' section).
Alternatively, you can force the gallery to be displayed in Large Screen Mode (which, by default, does not use the Splash Page) on all devices and in all browsers by setting screenMode="LARGE" ('Customize -> General').

If you choose to continue to use the Splash Page, you can customize it using the Splash Page configuration options.

All you need to do is start your backButtonUrl with 'http://' and the entry will be treated as an absolute path.
Change:

backButtonUrl="www.yosemitecollection.com"

... to:

backButtonUrl="http://www.yosemitecollection.com"

If the backButtonUrl does not start with either 'http://' or 'https://', then the entry is treated as a relative path (relative to the HTML page containing the gallery's embedding code).

Setting your backButtonUrl to 'http://www.yosemitecollection.com' should solve your problem.

Your gallery seems to display and function fine for me at the moment.
It looks like you might have solved your problem (or perhaps there was a temporary glitch with either your web server or internet connection which was contributing to your problem).
If you currently cannot see the gallery on your web page, try clearing your browser's cache before reloading your web page to see if this makes a difference.
If you continue to experience difficulties, then please let me know and I'll try to help further.

It may still be possible to open images with a lightbox script other than Shadowbox but Shadowbox made it easy by allowing its lightbox to be opened via a custom JavaScript call.

If you are still interested in using Shadowbox, then you should be able to download the files from the GitHub page here: https://github.com/mjackson/shadowbox

It should certainly be possible to load a Juicebox gallery into a lightbox as long as the lightbox script in question supports displaying HTML pages (rather than just images) as a Juicebox gallery needs to be embedded in an HTML web page.

As far as I am aware, Lightbox does not support displaying HTML pages.

An alternative to Shadowbox for this purpose would be SimpleModal.

To see an example in action, create a sample gallery with JuiceboxBuilder-Pro, use the following code for the gallery's 'index.html' file and include the jQuery and SimpleModal JavaScript files in your gallery folder.
Then, open the 'index.html' page in a browser and click the 'Gallery' button to open the gallery in a SimpleModal overlay.

<!DOCTYPE html>
<html lang="en">
    <head>
        <meta charset="utf-8" />
        <meta name="viewport" id="jb-viewport" content="minimal-ui" />
        <style type="text/css">
            body {
                margin: 0px;
            }
            #juicebox-container {
                display: none;
            }
            .simplemodal-wrap {
                overflow: hidden !important;
            }
            #simplemodal-container {
                background-color: #333333;
                border: 8px solid #444444;
                height: 400px;
                padding: 12px;
                width: 600px;
            }
            #simplemodal-container a.modalCloseImg {
                background: url('simplemodal/x.png') no-repeat;
                cursor: pointer;
                display: inline;
                height: 29px;
                position: absolute;
                right: -16px;
                top: -15px;
                width: 25px;
                z-index: 3200;
            }
        </style>
        <script type="text/javascript" src="jbcore/juicebox.js"></script>
        <script type="text/javascript" src="jquery-1.11.2.min.js"></script>
        <script type="text/javascript" src="jquery.simplemodal.js"></script>
        <script>
            $(document).ready(function() {
                $('#link').click(function() {
                    $('#juicebox-container').modal({
                        onClose: function (dialog) {
                            dialog.data.fadeOut('slow', function() {
                                dialog.container.hide('slow', function() {
                                    dialog.overlay.fadeOut('slow', function() {
                                        $.modal.close();
                                    });
                                });
                            });
                        },
                        onOpen: function (dialog) {
                            dialog.overlay.fadeIn('slow', function() {
                                dialog.data.hide();
                                dialog.container.show('slow', function() {
                                    dialog.data.fadeIn('slow');
                                    new juicebox({
                                        containerId: "juicebox-container",
                                        galleryHeight: "100%",
                                        galleryWidth: "100%"
                                    });
                                });
                            });
                        },
                        overlayCss: {
                            backgroundColor: "rgba(0,0,0,0.5)"
                        }
                    });
                    return false;
                });
            });
        </script>
        <title>Test</title>
    </head>
    <body>
        <div id="header">
            <input type="button" id="link" value="Gallery" />
        </div>
        <div id="juicebox-container"></div>
        <div id="footer">
            <span>Other content</span>
        </div>
    </body>
</html>

If you want to open an image from within a gallery in a lightbox script, then this would be more complex and I have only had success doing so with Shadowbox (as noted in my posts above).

Perhaps other users have tried this with other lightbox scripts and can help out further.

Out of interest, what version of Windows are you using?
Is there anything out of the ordinary about your setup?
Do you use multiple hard drives? If you do, then try to ensure that both Adobe AIR and JuiceboxBuilder-Lite are installed on the same drive (the drive containing your operating system).
Also, try creating a fresh Admin User Account and try installing JuiceboxBuilder-Pro under the new account, just in case there is something wrong with your current user profile which is contributing to your problem.

You currently have WP-Juicebox installed and activated.
The plugin is loading the 'juicebox.js' v1.4.1 file into the <head> section of your page and your manual embedding code loads the 'juicebox.js' v1.4.3.2 file into your page. The two different versions of the 'juicebox.js' file may be conflicting with each other.
When embedding a gallery manually into a WordPress page or post using the baseUrl method, it is not necessary to have WP-Juicebox installed and activated at all so try deactivating the plugin to see if this help.

In order to display images in a Juicebox gallery, the images need to be uploaded to a web server somewhere.
Many users have their own web space where they can upload their gallery folders (which include core Juicebox files and images).

You could perhaps sign up for a hosting account with a regular web host which would allow you to upload your Juicebox galleries to your own personal web space using a dedicated FTP program such as Filezilla.
There are many web hosts that offer free web space which would be suitable for hosting Juicebox galleries.
Try a web search with terms such as 'free web hosting' but please bear in mind that with a free hosting account, you will likely get little or no support, less reliability (more server down-time) and fewer features.

Also, you could host your images on Flickr.
Juicebox can be configured to display images from a Flickr account (using tags or sets to display only certain images).
For reference, the Flickr options supported by Juicebox-Pro can be found here.
You can quickly and easily create a Juicebox gallery sourced by Flickr images using JuiceboxBuilder-Pro.
On the 'Images' tab, choose 'Flickr' as the 'Image Source', enter your Flickr Username or Id and click 'Load Images'. You can then configure your gallery as required (on the 'Customize' tab) and save it (on the 'Publish' tab).
Please note that you will still need to upload the core Juicebox files (as well as an HTML page containing the gallery's embedding code) to a web server somewhere but the images will be taken care of by Flickr.

If you do not have any web space at all, then you could host a gallery on Google Drive following the instructions here.

Take a look at the Getting Started support section which should help you install JuiceboxBuilder-Pro.
You could then quickly and easily create a Flickr gallery by going to JuiceboxBuilder-Pro's 'Images' tab, selecting 'Flickr' as the 'Image Source' and entering your Flickr User Name (or Id).

If you do not already have a Flickr account, sign up for one (its free) and upload a couple of test images before trying out JuiceboxBuilder-Pro.

The Juicebox plugin for WordPress can be downloaded from this web page. Installation and usage instructions can be found on the same page.
If you get stuck with anything specific, just let me know and I'll try to help you out.