Sounds like you need to set boundries or she will feel she can waltz in and out of your home and life whenever she feels like it.
If you have an email address for her, email her. Let her know that all future dealings and activities involving the children will be done through you, not through your children. If you don't have an email address, then call her yourself.
I would also let her know that when she comes, she best have a motel reservation, so she has a place to stay. She may not like that, but she no longer lives with you, and shouldn't expect that you would put her up when she is in town.
I am sorry you are having to deal with all this roller coaster divorce crap. She sounds like a person who didn't understand what a gem of a husband she had. She also sounds very selfish and everything is all aobut her...except the blame for her actions.
Don't allow her to dump her guilt on you. As many others have pointed out, you did nothing wrong. You are the strong and steady one. She is the one who moved out to be with another man.
Set your boundries of what you will and will not accept and allow. Time to draw that line in the sand. If you haven't started the divore process, you need to get moving on that. You don't want to be held responsible for any debt she is or will incurr with this man.