You are correct with your setup and (a) assumption; with a combined DSL modem/router device like your 2wire you need to leave it all alone and use the T-Mo router like you have it; you can't make the setup change I recommend due to the combined device without a bunch of work (but it IS possible) - if your UMA is working STOP, quit tinkering.
For completeness sake - what you'd do is:
1) scrape all config settings from the 2wire webUI into a notepad (usernames/passwords, ISP connection method, etc.)
2) configure T-Mobile device as a router, reboot it, then put in all settings from the 2wire gleaned in step #1 (it is best do do this step with the T-Mo unplugged from everything and wire in directly to it for initial setup from your PC - pretend you just pulled it out of the box)
3) change 2wire config to act as a bridge and not as a router - this changes the device to 'dumb' mode, all is does is transform DSL copper into ethernet for you, so to speak.
4) plug in your T-Mo router to the 2wire, turn it on and see if everything works
5) set up wifi on T-Mo, BB, etc. now that it's all working
Really it's not too hard if you're familiar with the basic networking concepts, but in practice I have friends who don't "get it" and need a guy like me to come over and help them out - not everyone is a nerd.