A frame-driven website is likely to be less than optimal on mobile devices (as you have discovered) and, additionally, there are drawbacks to loading a Juicebox gallery into an frame. These drawbacks are noted here (scroll down to "2) Using an iframe").
If possible, it would be much better to layout your page using CSS rather than frames and to embed the gallery directly into the web page following the embedding instructions here.
If you are looking to have a web page with a side menu, then I would recommend taking a look at the View Resizable Gallery with Side Menu Example in the Using a Resizable Gallery support section.
You can view the source of the sample web page in your browser and copy/modify it to suit your own needs.
If you are looking for an automated way to create your complete website, you might be interested in another one of our products, namely Showkase.
Showkase is a PHP web application (installed on your web server instead of your computer) which allows you to create a complete portfolio web site (integrating multiple galleries) online.
Showkase has full support for Juicebox-Pro and the galleries can be created within the application itself in a web browser interface (or created with JuiceboxBuilder and imported).
You can create Gallery Index pages and have as many galleries listed on each Gallery Index page as you wish.
Each gallery is represented by a thumbnail image with the gallery title displayed below and the gallery is opened when the user clicks on the image.
Demo sites created with Showkase can be found here and a sample Gallery Index page can be found here.
Showkase can also create non-gallery pages (About, Basic and Contact pages) where you can add information about yourself (or any other content you like).
All of this is done automatically within the Showkase interface without the need for any manual coding at all.
You can check out the Showkase interface by logging into the Live Demo Admin.
Showkase comes with several different themes, (Boma, Kosel, Maribo) and Boma features a side menu (whereas Kosel and Maribo both feature a top menu). Here is a sample site created in Showkase with the Boma theme.
Showkase can be purchased as Showkase-Standard (which comes with Juicebox-Lite, the free version) or Showkase-Pro (which comes with Juicebox-Pro).
The only difference between Showkase-Standard and Showkase-Pro is the bundled viewer (Juicebox-Lite vs Juicebox-Pro).
I hope these notes help.