In your gallery's 'config.xml' file, you currently specify the backButtonUrl and splashImageUrl with absolute paths using http:// rather than https://
Change your paths to use https:// or scheme-relative URLs (starting with //) instead.
For example, change:

splashImageUrl="http://www.countyfairgrounds.net/images/139_10.jpg"

to either:

splashImageUrl="https://www.countyfairgrounds.net/images/139_10.jpg"

... or:

splashImageUrl="//www.countyfairgrounds.net/images/139_10.jpg"

Also, in your gallery's embedding code, change:

<script src="/jbcore/juicebox.js"></script>

... to:

<script src="//www.countyfairgrounds.net/jbcore/juicebox.js"></script>

I notice that you have other http:// links in your web page (in your <div id="sociallinks"> container) that you may also need to change.

You're welcome!

I'm glad you've solved your problem. Thank you for letting me know.

Please post the URL to your gallery so that I can take a look.
Also, if possible, please provide screenshots (perhaps upload them to your web server or a file sharing service such as Dropbox) so that I can see what you are seeing.

I would really need more information to troubleshoot (or explain) what you are reporting (e.g. the version of Juicebox you are using, the dimensions of the gallery, the dimensions of the thumbnails, the gallery configuration options, etc.)

In the meantime, here are a few notes which might help.

Please make sure that you are using the most recent version of Juicebox-Lite (v1.4.3.2) to ensure that any bugs from previous versions are not contributing to the problem.
If necessary, instructions for upgrading can be found on the Upgrading Juicebox support page.

If you are using a percentage height for your gallery, then please see this note or try using a fixed pixel height instead instead.

Do you see the problem in any of our demo galleries here?

Hopefully with a little more information, I'll be able to figure out what's going on.
Thank you.

You're welcome!
I'm glad it's working as expected now. Thanks for letting me know.

The way that WP-Juicebox currently works is that each gallery is associated with a single page or post and, if the Media Library is used as a source of images, then the images attached to the page or post containing the gallery will be displayed.
Unfortunately, there is no easy solution to change the way that WP-Juicebox works.
However, rather than try to separate galleries from their pages or posts, it would be possible (with knowledge of PHP and WordPress functionality) to change the way that WP-Juicebox displays Media Library images.
One possible solution might be to tag images in the Media Library (with a third-party plugin which allows such functionality as WordPress does not natively support this) and modify WP-Juicebox so that each gallery displays only images with specified tags. However, this would require a lot of work (and it would work only with a specific tagging plugin of your choice as all tagging plugins use different terms for their tags).

It would certainly be possible to extend WP-Juicebox to use a new source of images (such as FooGallery) but an in-depth knowledge of how FooGallery works would probably be required (at least knowledge of how and where FooGallery stores images or image data) and I am not familiar with this plugin.

You could certainly manually embed Juicebox galleries (created by JuiceboxBuilder) in WordPress pages or posts using the baseUrl method of embedding documented here.
Essentially, once you have created a gallery with JuiceboxBuilder-Pro, you would upload the complete gallery folder (not just the contents) to your web server and paste the baseUrl embedding code into the body of your WordPress post (ensuring that the method of entry is 'Text' rather than 'Visual'). It does not matter where on your web server you upload your gallery folder to as long as the two paths in the embedding code (the path to the 'juicebox.js' file and the baseUrl itself, pointing towards the gallery folder) are correct.

As you are already using Lightroom, maybe you'd like to use the Lightroom plugin (which comes bundled within the Juicebox download zip package) to create your galleries (rather than JuiceboxBuilder). This might be better suited to your current workflow. More information about the Lightroom plugin can be found here.
I don't know if my notes above will actually help but I hope they might at least clarify a few things or point you in the right direction.

The latest version can be downloaded from the WP-Juicebox support page here.
The WP-Juicebox Version History can be found here.

If you want to prevent browsers from caching your gallery's dynamically-generated XML file, then try adding a unique query string (e.g. the current time which will be different each time the browser loads the page) to the configUrl option in your gallery's embedding code.
For example:

configUrl : "config.php?nocache=" + new Date().getTime(),

If you really want to add a refresh button to your web page, then you could use something like the following (which would overlay a 'refresh' link in the top left corner).

<div id="refresh" style="background-color: rgba(0,0,0,0.5); color: rgba(255,255,255,1); cursor: pointer; font-size: 20px; left 0px; padding: 4px; position: absolute; top: 0px; z-index: 9999;">
    <span onclick="javascript: window.location.reload(); return false;">Refresh</span>
</div>

If you wanted the 'refresh' link to be displayed only on mobile devices, then you could check to see what screen mode Juicebox is using (via the Juicebox-Pro API getScreenMode() method) and display the 'refresh' link only in Small Screen Mode.

<!DOCTYPE html>
<html lang="en">
<head>
    <title>Juicebox Gallery</title>
    <meta charset="utf-8" />
    <meta name="viewport" id="jb-viewport" content="minimal-ui" />
    <meta name="description" content="This is a Juicebox Gallery. Get yours at www.juicebox.net" />
    <style type="text/css">
    body {
        margin: 0px;
    }
    #refresh {
        display: none;
    }
    </style>
</head>
<body>
    <!--START JUICEBOX EMBED-->
    <script src="jbcore/juicebox.js"></script>
    <script>
        var jb = new juicebox({
            containerId: 'juicebox-container'
        });
        jb.onInitComplete = function() {
            if (jb.getScreenMode() === 'SMALL') {
                document.getElementById('refresh').style.display = 'block';
            }
        };
    </script>
    <div id="juicebox-container"></div>
    <!--END JUICEBOX EMBED-->
    <div id="refresh" style="background-color: rgba(0,0,0,0.5); color: rgba(255,255,255,1); cursor: pointer; font-size: 20px; left 0px; padding: 4px; position: absolute; top: 0px; z-index: 9999;">
        <span onclick="javascript: window.location.reload(); return false;">Refresh</span>
    </div>
</body>
</html>

(onInitComplete() and getScreenMode() work in Juicebox-Lite as well as in Juicebox-Pro.)

I hope this helps.

This is what makes me think that the 100% height is the root of the problem.

This should not make a difference. There are no duplicate ids on the page and the gallery is already correctly embedded into a div with a unique id.

Unless otherwise specified, vertical scrolling should already be enabled on the page as the default value for the CSS overflow property is visible.

Clicking the 'Photo Gallery' tab calls the loadGallery() function but the gallery's embedding code is not within such a function wrapper on your web page. (Currently, the gallery's embedding code is run as soon as the web page is loaded and when this happens, the gallery's parent container is not visible on screen and has no dimensions.)

Change:

<script>
new juicebox({
containerId: "juicebox-container",
baseUrl : 'owl_slide/',
galleryWidth: "100%",
galleryHeight: "100%",
backgroundColor: "rgba(252,242,204,100)"
});
</script>

... to:

<script>
    function loadGallery() {
        new juicebox({
            containerId: "juicebox-container",
            baseUrl : 'owl_slide/',
            galleryWidth: "100%",
            galleryHeight: "100%",
            backgroundColor: "rgba(252,242,204,100)"
        });
    }
</script>

This should hopefully solve your problem.

Thank you for creating a new test page.

I have just checked this page in Chrome 42, Firefox 38.0.1, Internet Explorer 11, Opera 29 and Safari 5.1.7 on my PC and the text and video (and gallery) all display fine and stay visible in all browsers.

The only potential problem I see is that you have given your gallery a percentage height (100%) and your gallery does not have a parent container which has been assigned a height via CSS. Therefore, the browser may not be able to determine what the gallery's actual height should be 100% of. (Maybe the browser is using 100% of the entire viewport and covering the other elements on your web page with the gallery.)
Please also see this note regarding Using Percentage Heights.
Try giving your gallery a fixed pixel height (perhaps 600px) instead to see if this helps.

I posted an example of how you could do this here: http://juicebox.net/forum/viewtopic.php?pid=8161#p8161
The code I posted takes into account the location of your 'jbcore' folder (in your root directory).
Give it a try. I've already tested it out in a text widget (like you are using) and it works fine.
Just create your two gallery folders, upload the complete gallery folders (not just the contents) to your root directory (alongside your 'jbcore' folder) and copy the entire code from my post into the text widget making sure that the 'id' attributes of the links are the names of the gallery folders ('winter' and 'summer' in my example).
You can choose to use the Splash Pages (or not) within each gallery via the showSplashPage configuration option.

(You could choose to relocate your gallery folders anywhere on your web server but you would need to compensate for this within the code. The code will work fine as it is as long as the gallery folders are in your root directory.)