That isn't possible, only the cache and the bookmarks.html file can be moved to a different location in Firefox.
{I relocate both of those files myself on almost every Profile I run; I have investigated moving other files but haven't been able to find others that can be moved.}
There are extensions to allow you to "sync" Profiles on different PC's, but none that I am aware of that don't use online storage of the files to be synchronized. IOW, none suitable for your situation.
The only solution that I can think of is to use the entire Profile on the USB stick on your home PC with a Command Line Argument directing Firefox to launch using that Profile. -
http://www.mozilla.org/docs/command-line-args.html
But it would be easier to just use the entire Portable Firefox on both computers, than to have your home PC be launched with the Portable Profile.