We've been with you through this, D., and it sounds like maybe you're just having a moment. Is your counselor giving you specific tools to move forward? Maybe you should see an actual psychotherapist. If you still want to fight for this particular marriage, you have that right, but you'll need to hold his feet to the fire and force him to make some major decisions. You can't let him continue to "ride the fence" because he'll do just that. Also--food for thought--men generally do not leave one relationship until another is waiting for them, so just because he seemed happy doesn't mean that all was well. Sometimes it takes an outside force to spark something, and some people just don't understand that that doesn't necessarily mean that you should leave. It's not her fault, but she is definitely influencing him because she doesn't want to look like a fool, having left her husband for him.
I don't any more particulars than what you've shared here, but I think that you should let him know that you want your family back together but that you will not make it easy for him to avoid moving forward on one side or the other. He needs to get off to himself for a while, with no contact with her. Meanwhile, you have to avoid being his soft place to land and shoulder to cry on. He doesn't get to have that from you if he can't muster up enough to respect than what he's displaying. He has a right to go through this process of figuring himself out, but eh does not have the right to drag you and your children through it. When it's to the point of disrupting the fmaily, then he has an obligation to go off by himself to fix it, even with your assistance, since you would be his wife. When he brings someone else into the mix, you are no longer obligated to help him.