I read your sitch and first you have come a long way...don't ever discount that. I can't imagine how you must have felt and what you must have gone through being pregnant and discovering that. Don't ever (also) doubt how much crap your H has put himself through for that. Men always want to be seen as a good father and a good man and he probably has put himself through the ringer for that...

So the way I see it there's three things that could happen:
a) you get back together he never talks to OW again
b) you don't get back together and he stays with OW forever
c) you don't get back together and moves on with someone else.

in all of those outcomes you two will still have children together and be around each other AND he'll still have that tattoo.

For a very long time I let myself ruminate about how H was doing things with his GF and not with me, how big events were happening in the UK and I would always remember that he was with someone else during those times. You have to let go. You have to decide to forgive...even if you never get back together, because it will eat you up and tear you up inside. You are almost LOOKING for something to trigger your pain. The tattoo which you say you've seen before, but because he took off his shirt and you saw it you decided to concentrate on it rather than the fact that you were having a happy family day out together.

My DB coach told me I was real good at seeing the bad IE he may have done something amazing, but he didn't do it right, or he had to ask me for something or whatever. She said to work on seeing the good and it's made a world of difference. She also said to find anything to be happy for him. And so even though he went to a music festival with her that we'd talked about going to and that some of my favorite bands were playing at, I decided not to be jealous or resentful and instead said I'm really happy you're getting that opportunity. I hope you have a lot of fun. And you know what I found myself being happy for him.

The fact is the affair happened. Nothing now, will change that, but you change how you decide to live with that having happened now.

Someone much wiser than me posted that if you are ever going to have a R in the future you have to forgive and let go or there's no point in being married. you'll just be together and be miserable.

I decided in my head that H and I were over, that all he was offering was friendship and I could accept that and enjoy it or I could sit on my high horse (alone) and punish him for his decisions and his rejection of me. Right now, your H is offering you friendship and co-parenting, can you accept that if that's all that's ever offered?