Lenny listen to Joseph you need to choose a Bais Din that is impartial. I think she is going to claim abuse and hopes they will accept it. If you agree to her Bais Din they may agree with her. I think she is trying to pressure you into giving a get as that is the only option. You need to speak to a divorce lawyer and find out whether the fact that she is not cooperating with the marriage counselor is grounds to dismiss the case or punish her in some other way.
How are the children handling this breakup? I hope you are not using them as an intermediaries to communicate with your wife.
As I said previously, go back to the Rav from Bais HoRa tell him you thinking of giving a get but you need to know what the financial obligation and custody will be. The Rav can negotiate for you a better settlement then you would get in Civil Court. Also you wouldn’t be paying for two lawyer to litigate the divorce at $200.00 + per hour.
Wishing you the best Good Shabbos