Normally, I would say "no kids, then run", but in this case you don't want kids, which changes it somewhat, and you have been together a long time. You don't have to make any decisions right now, you can sit on this.
OTOH, I think I would run.
I had 4 kids and the aftermath of the betrayal was awful and is still triggery many years out despite reconciliation and a truly remorseful FWS.
But, as another poster reports, I don't think I will ever feel that "special" in my marriage again since the affair, although I do feel loved, I recognize that the damage can never be fully undone, and the terrible things that were done to me in the betrayal and afterward leave one with nagging uncertainties.
Another thing I learned, which is simply not a good thing to learn, is that my FWS and I have this hierarchy of importance in the immediate marriage. Oversimplified below, but take it for what it is worth, listed in order of importance.
Her: Children, herself, me, pets, property.
Me: Her, children, myself, pets, property.
The affair was 19 years ago. If you had asked me 20 years ago, 10 years ago, perhaps even 5 years ago after 4 years of MC, I would have thought her ranking me was the same as my ranking her. There was a grim recognition around 4-5 years ago that I was never #1, not at any time, and never will be.
All the MC in the world doesn't change that, didn't change that. All our children are now grown, that didn't change it either. She is wired that way. I am wired the way I am wired.
MC did change the destructive behaviors and approaches to the marriage, but it didn't change my position. I never made any decisions without considering impact to her and the children first and foremost, but she did make many decisions without considering the impacts on me.
Consider your place in his life, your real place, where he places you, not where you place him.