If so, think seriously about how you want to deal with him this time.
It may be time to stop "wooing" him back and time to just move on.
I'm not saying he's irredeemable; but so long as he can dither around thinking he has a CHOICE between you or OW, he'll dither. You've done your 180s, you've DBed your behind off, you've created good new memories with H. Maybe it's time now for him to feel the reality of what he's going to lose by his continued involvement with OW (and make no mistake, he's still involved).
You need to be sure you're ready before you LRT - that you are okay with the possibility that he won't turn around. Trust me, if he's not really capable of becoming a better man, you don't WANT him to be the father of your children.
No anger, no scenes. Just "You know, H, I think I deserve a man who loves me and wants to be with me alone. Since you can't be that man right now, I think it's time for me to move on and look for a man who can".