Hi AND-01! Welcome to the family!
Many of us here have been (or still are) in your shoes and we're happy to help.
It sounds to me like you're doing so much right. You're taking care of your children. You're seeking therapy for yourself and encouraging her to do the same. You've educated yourself and built up a support system. That's all awesome! As you know, these relationships can be difficult and you're equipping yourself to deal with whatever happens.
Affairs and loss of trust deal terrible blows to any relationship, unfortunately.
I don't have an answer on whether or when to address the infidelity but someone else here may have some insight and experience to share. Have you asked your counsellor about that? Does he/she have any thoughts?
It sounds like you're sort of stuck in a holding pattern at the moment, not sure what to do. Have you given thought to how long you're willing to wait for improvement? And what that improvement should look like?
I hope you'll keep posting and reading in others' threads. You'll find that quite a few others here have dealt with infidelity and have experience to share. You may have some advice to help fellow posters as well.