I am so sorry this happened to you. Take care of yourself; you've been through such a great shock.
Take your time deciding what you want to do about your H, if you should decide to D. That's not a decision that needs to made today.
What I do think is important is for you to establish communication with your H and get his passwords for everything.
I don't believe for one second any reputable therapist would tell a man not to contact his wife. I think your H is gassing you. Get a hold of him and remind him you are the wife and if he goes NC with anyone it's the ONS. How dare she talk to him? As if they are co-parenting? It makes me sick.
I know you said you love him and are in love with him. That's completely natural. You don't automatically fall out of love with your spouse.
Add in the shock of this intruder in your life and the lies and the sheer cruelty of shutting you out of the conversation and no wonder you don't know what to do, where to turn to and who to trust.
I think it's a common default to try to save the M and to wait and see what happens. Ironically, I think people who take a much harsher approach about what treatment they accept after DDay have the better outcomes regarding saving the M.
IMO, the ones who initiated D proceedings (even though they eventually stop the process) and those who told the WS to start packing are more likely to successfully reconcile.
Your H needs to know in no uncertain terms that he needs to work immediately to reestablish trust. There are consequences to his actions and fretting over what new girl or her mother thinks is something a coward would find refuge in.
A softer approach seems to fail pretty pretty consistently.
It's my opinion your H needs to get on the next plane back home and take things seriously with you. The new girl has no urgent needs on his time, none whatsoever, but you do.
I think your first steps should be to a family lawyer to make your own will. You may try to set up trusts for your children in case you precede your H in death. Your assets go directly to them.
Yes, new girl will probably definitely look into inheriting from her new bio parent. I wonder if she wants new bio dad to pitch in for the wedding. You need to be in the loop.
I think you should also see and attorney about separation and D. Do not make any threats you are not willing to follow through. Since your H does not seem to want to leave you, maybe being served would get his head unstuck from the butt it's currently jammed up in.