I have done 2 rounds of DBT @sarvan and it is something you need to be focussed and ready for. I was very reluctant to do it because I did not think I would cope - especially being in a room of strangers when I was not feeling safe within myself. It is not an easy course to take and you do need to be really focussed on not only the theory but also being able to put it into practice after each session.
Can I ask if you had a counselling session straight after the DBT session? From what I understand and from personal experience the optimal benefit comes from doing a session then talking with a counsellor/psych/pdoc afterwards. I had sessions with my pdoc directly after and it was in those sessions that I was able to discuss not only what we dealt with in the DBT session but any difficulties I had.
We also had one member who left the group as she was much the same as you - constantly triggered, crying and unable to take anything in. It was really uncomfortable for the rest of the group and the facilitator made that decision for both her and the remainder of the group. I very much hear where you are coming from but also know that sometimes we are not ready for the type of therapy we are undertaking - I myself was constantly re-traumatised by exposure therapy and then EMDR so it was for my benefit to stop. I am much better without them and have been able to move forward by concentrating on the things more present in order to cope.
One of the things about any form of therapy is we have to be able to cope with what we are engaged in so I would say do not give up on DBT (it certainly helped me) but instead work with your counsellor on how you can manage it and your emotions to get the most out of it in the future.