Studies have shown that the single biggest predictive factor for success isn't actually the type of therpay or therapist. Although those things are important, the quality of relationship between client and therapist is the single biggest predictive factor of successful therapy and reduction of symptoms. A good relationship doesn't mean there are never bumps in the road but that the three pairs and client are able to work through them, and in the case of trauma, have what is called corrective emotional experiences.
I have found it much easier to do effective therapy for trauma with someone who understands dissociation and is trained in more than one trauma technique. It works out better.
When I couldn't find a trauma therapist I did find a therapist that I was able to build the best relationship with. It wasn't as effective as the work I have done with a trauma therapist, but it still helped a lot.
In a nutshell: it's beneficial but not required. What is almost required us a therapist you click well with. If this therapist isn't able to work with you to work through this, and you can't find a trauma therapist, then mayhe you could try meeting with a couple other therapists and see if works better,