As AllHeart said, it is ultimately your decision on what to do, but the T's concern is understandable.

I just want to add that many Ts feel uncomfortable working with trauma directly because the general training unfortunately doesn't give them skills and solid background for doing trauma work. Only those Ts who have gone through specialized training like EMDR, neurofeedback, somatic experiencing and some others have a solid understanding of trauma in the first place, understanding that is based on scientific findings, as opposed to speculative theories Ts mostly use. Considering the lack of general knowledge and skill level, it's actually a good thing that your Ts is reluctant to proceed with trauma work. Frankly, if she hasn't received any specialized training in working with trauma, I wouldn't consider doing this kind of work with her. I'd look for a specialist if you feel like trauma work is what you need.

Also, you need to be realistic about how much you can achieve as a result of trauma work. If you are hoping that you will be able to release all the trauma from your system, you'll be highly disappointed because it's not possible. Trauma healing is a life time work, not a result of a brief intervention. You CAN certainly achieve SOME progress and feel much better, but there will always be remaining traumatic material to work on, so this is something you need to accept from the get go. Nothing and no one can miraculously heal all your wounds.

And, in order to achieve SOME progress in that direction, you need to commit yourself to a long-term process, not necessarily with the same practitioner, just
to the process of doing the work throughout your life time. It's best to take it slow, as slowly and as gradually as you can in order to solidify the results and to make them last. This is really the case when slow and steady wins the race.