I think the ex is being over-sensitive, but you still have to deal with that since you are married to the children's father.

If I were you, I'd write her a letter something like this:

I want to apologize to you if I have overstepped boundaries. However, you must understand that this is a new situation for all of us and we are still learning.

In particular, I want to apologize about the prom dress. The situation seemed to spiral out of control so quickly - in future, if such a situation occurs, how would you like to handle it?

As far as my relationship with your children - would you prefer I was indifferent to them or disliked them? Right now, I have a positive relationship with them. While I am not their mother and would never presume to take that role, by being on good terms with your daughters I am providing them with another adult who cares about their wellbeing.

Hopefully over time we will get through these growing pains and be able to provide the positive environment your children deserve.