Kudos on moving on quickly when you knew you weren't/couldn't get what you needed from T1. It sounds like you need to give T2 constant feedback (inc questions inc "why are we doing this?") initially, & perhaps keep any uneasiness you are aware of working with a woman on the table for awhile ... so a longer breaking period ...

But after that, no reason you shouldn't do your best work yet with her. What are your main concerns at this point?