I remember this exact situation before. B wanting to reconcile and you not being sure. What I see is B "wants" to but he is unwilling to "try". His multiple attempts and regressions suggest he is only going through the motions to get what he wants.
My advice... move forward with your life and see if he follows. If he does follow set boundaries. The things you will and more specifically will not tolerate. Let him know he has one chance left. If he blows it, you are done with him. I'm not suggesting you immediately open your arms and heart to him. What I'm saying is you build your trust over time. I'm really doubting he can pull it off, but I'm never one to say, let him go. That's your call.
I hope the kids are well. I know baseball must be in full swing right now and you are as busy as can be. Let me know if you want to talk and I'll send my contact info.
