I'm sorry you have to deal with this.
I'm sorry your H has to deal with this, too, because he's in for a very difficult, painful time unless he can pull himself back from limerence.
The thing is: probably the only way out of long distance limerence is to go what we call 'No Contact' or 'NC'. But your H is maintaining, not ending, contact.
I do think it's possible to fall in love with a voice on a phone or video call. I actually did fall in love with a voice in an in-person class, but her voice grabbed me on the phone, too. We were both unattached when that happened, though, so it was more than OK. (She had an A 45 years later, but we dealt with it.)
What are the conditions under which you would take your H back? Write them down and share them with him if he decides he just has a crush. If he signs up to meet your requirements, you've got the basis of reconciliation. If you can't agree on what your new M will be, you don't have a basis for R.
I agree with Cooley: talk to some good family of D lawyers.
*****
I know the pain is excruciating. All I can offer is my opinion that feeling the pain lets it go, and that's the best course of action open to you. But yeah, being betrayed brings along with it immense grief, anger, fear, shame, and other feelings, too.
You can process the feelings out of your body. A good IC can help. There are some methods that you can do on your own, like 'EFT', Emotional Freedom Technique.
Have faith in yourself to heal. You are stronger than you think you are. It also looks like your kids are good sources of support. Kids demand a lot, but every so often, they give a lot, too.
*****
BTW, you've taken some steps that are highly recommended: 1) refusing to engage while the A is ongoing, and 2) setting a deadline.
IMO, courage and patience are great helps to surviving and thriving after infidelity, You've made a good start.
[This message edited by SI Staff at 11:16 PM, Sunday, August 16th]