First, I am sorry to hear of your issues with a dissolving marriage. I agree with the advice posted above, including that your ex may try to sabotage any new relationships.
Second, it's time to hire a lawyer. There's often a lot of nonsense that happens in a dissolving marriage. It is in your favour that you don't instigate or respond in kind, as the judge will see through it if it comes to going to court.
Continuing counselling for the time being is a good plan. Your ex's betrayal of trust is something that needs processing over time. It's too soon to get into another serious relationship. Give yourself significant time to heal, like six months or more.
Crossdressing is not an acceptable excuse for cheating, IMHO.