I see two T's-- one is psychodynamic the other is more cbt based---the cbt guy is focused more on my health and anxieties.

Actually, my health T does therapy with some cbt components, not full cbt with worksheets. But I do get a sort-of homework. Usually some kind of exposure to my anxieties.
We talk about the homework, and he will usually assign me a new task.

If I can't do the homework, we will discuss why and he will find a more "do-able" goal.
We take things pretty slow, which I like.

I wouldn't downplay trauma--it is a big deal. Give yourself time to open up and let your T know your worries (I worry about being abandoned and being judged)