I understand the problem.
You'll have to keep switching the iPad's account back and forth to transfer apps from each account. It will only transfer the apps associated with the account you are currently logged into. Or so I understand from other posts. I haven't any personal experience.
It might be necessary to log into the same account on the computer's iTunes also.
Friend or not, you should seriously consider the position you are putting each other in by keeping the apps.
Addendum, I just logged in to the app store on the iPad using my "mac.com" address instead of my usual email. That worked, such that I can now see those apps that I've "installed". So that's good.
Still can't get them to sync to my desktop but at least I can redownload them if I change iPads.