It’s interesting that there are posters on here who would end a friendship if they found out that the friend had had an affair, or at the very least would think less of them. And yet a poster has an affair and leaves for that man and her children should get used to it?
OP, it doesn’t matter whether you’ve explained it to them. Fact is, you left their father for another man and now you’re expecting them to want a relationship with him.
While I agree that relationships do end and that sometimes those relationships end because of affairs, the fact is it was your choice to cheat on their father, and as such it is unreasonable to expect them to welcome the OM into their lives.
Continuing a relationship off the back of an affair is always going to be messy. FWIW I’m not judging the fact that you had an affair, but your decisions were inevitably going to influence your children, and let’s be honest, “we were unhappy for years” is often one of the oldest scripts in the book to justify infidelity.
I would say that even though your children will soon be adults, you do have to choose. Because if you want a continued relationship with them as adults and they refuse to have anything to do with your partner because of what he represents, there is a chance you will lose them, and even potential future grandchildren.
It’s good that you’ve left your marriage, but the way in which it happened has now left casualties behind. You need to decide whether he was actually worth all that.