Is there a way to relocate non-user controlled teams in MyLeague? I can't seem to find a way to do so. Also, I can't seem to find an option to change user-controlled teams.
1. No. 2. You can't change user-controlled teams after you've already started.
What you'll want to do is, when you start MyLeague, set every single team to be user-controlled, and then just automate everything for all of them except the one you want to mainly use, and that way you can trade between them without having to control them.