Your homepage seems to use a custom page template for display. The free version of WPtouch cannot be made to pick up that template but what you can do is to set your home page to be a listing of your latest blog posts. If you do not already have a page for that in your desktop theme, simply create and save a new, blank page then select that page under Home Page Re-Direction > WPtouch Home Page.
Quick Cache can be optimized for mobile use in the same way that other caching plugins are. To do so, enter the user agents found under Advanced Options > Custom User-Agents to the "rejected user agents" areas in your caching plugin's settings. Remember to clear your plugin, browser, and device caches before retesting.