The first two images may have exactly the same width but the length of their corresponding captions differs slightly.
When using captionPosition="BELOW_IMAGE", the width of the caption area equals the width of the image so when a narrow image is being displayed, the caption may be split into more than one line.
Other than changing the captionPosition to OVERLAY, it is not possible to increase the width of the caption area.
However, you could decrease the font size of the caption (so that it all fits on a single line) by using something like:

<caption><![CDATA[<span style="font-size: 11px;">Charcoal on Paper "22.5" x "36"</span>]]></caption>

Alternatively, you could change the font-size globally for all captions by opening the 'jbcore/classic/theme.css' file in a plain text editor and changing the 'font-size' on line 201.

As far as I am aware, there are no immediate plans to incorporate Juicebox-Pro options into the interface of the Lightroom plugin, though it is technically possible and may be considered some time in the future.

If there is a certain combination of Pro Options that you use for all of your galleries, you could edit the plugin's 'juicebox.lrwebengine/config.xml' file and add the Pro Options as attributes to the opening <juiceboxgallery> tag so that each time you create a gallery with the plugin, these Pro Options are used and included in the generated gallery's XML file. This may save you from having to edit XML files after you create each gallery.

Set your gallery's width to 100% and try using the following structure on your web page:

<div id="wrap" style="width: 100%;">
    <div id="left" style="width: 25%; float: left;">
        <span>Content for left side of screen goes here</span>
    </div>
    <div id="right" style="width: 75%; float: right;">
        <div id="juicebox-container"></div>
    </div>
</div>

Are you trying to embed a Juicebox gallery in a theme's header?
If so (and you know the gallery id you wish to display), you should be able to use the following code in your theme's 'header.php' file.

<?php
    $JB = new Juicebox();
    echo $JB -> shortcode_handler( array( 'gallery_id '=> '2' ) );
?>

... changing the '2' above to the gallery id of your choice.
Alternatively, the following should also work:

<?php
    echo do_shortcode('[juicebox gallery_id="2"]');
?>

As you have discovered, the gallery's dimensions are tied to the gallery (being stored in the gallery's XML file) and a single gallery cannot be displayed twice with different dimensions each time. In fact, the same gallery should not be displayed twice on the same page because both galleries will create divs with identical names to be embedded into.
I would recommend creating a separate gallery for your theme and, if necessary, duplicating the gallery (with different dimensions) for use elsewhere.

The problem with your original code seems to be the extraction of the gallery id from your custom field as entering the code above (with the hardcoded gallery ids) seems to work fine. However, I would need to know more about the custom field you are using to help with the extraction process.

What is output if you echo $juicebox after defining it on this line:

$juicebox = get_post_meta( $post->ID, 'slideshow_embed', true);

For your subsequent code to work, the output would have to be something like: [juicebox gallery_id="2"]

File received, thank you. I've deleted your link above.
I'll take a look and get back to you in due course.

I have just tried using your Flickr User Name and Tag in JuiceboxBuilder-Lite v1.1.0 and it works fine loading 30 images.
Make sure you are using the latest version of JuiceboxBuilder-Lite (v1.1.0) and that you are entering the User Name and Tag correctly. For example, ensure that you are not pasting your User Name with a leading space which would result in a 'Flickr User Not Found' message.
If you need to upgrade JuiceboxBuilder-Lite, it can be found in the Juicebox-Lite zip package which can be downloaded from this page.
Also, make sure your firewall is not blocking JuiceboxBuilder-Lite from accessing the internet.

It sounds like your theme sets a fixed height for your page which you would need to change in order to add any element (whether it is a Juicebox gallery or something else) with a height of greater than 250px.
I am not familiar with WooThemes but perhaps there is an option in the theme's settings (within the WordPress Dashboard) to alter the page height parameter.
If you cannot find such an option, then perhaps the WooThemes support pages and forum may help further.

Thank you for providing the link to your website and galleries.
Interestingly, when I view your galleries in Chrome on my iPod Touch, the 'Request desktop site' option is greyed-out.
We will investigate further.

In your original site, go into your WordPress Media Library and look to see if there are any images attached to the post containing your Juicebox gallery.
If there are images showing as being attached to your post, go back to 'Edit' your post and click 'Update'.
If there are no images showing as being attached to your post, attach some (upload some first if you have to) and then go back to 'Edit' your post and click 'Update'.

This JavaScript error is generated because there are no images listed in your XML file.
Once you create a working gallery (with images), this JavaScript error will not be generated.

It looks like you have found a bug. Thank you for reporting.
I have logged a bug report.
Until the bug is fixed, the workaround is to ensure that the backButtonPosition and the galleryTitlePosition are not the same. Set one as TOP and the other as OVERLAY.