Well, let’s start with not acting like a family unit.
She wants to be a family, while she runs around behind your back. I don’t know if you are ok with that. So maybe you shouldn’t be pretending to be happy family. You live like you are not together. You have your time with the kids, she has her time, and you go out and GAL on your time. You go and enjoy yourself .
When it’s your time with the kids, you have a fantastic time with them. She doesn’t come along and ply happy family. Because you will not be in an open marriage.