Kelela, just current on this thread, so I do not know what precipitated your BD etc.
I would say read my thread but it's really long so I will sum up for you.
H and I split in September...ILYBINILWY ....haven't been for ( insert years here, because it varied).
Found out six weeks later that he was seeing someone else starting shortly after our split.
He continued seeing her for nine months and she broke it off when she asked him to choose between her and his friendship with me. He choose to have our friendship, but not before he threw me under the bus a few times in favour of XGF.
I asked that the children not meet her. Seven months in he said it was serious and talked about moving in together. I said that we would have to be divorced, and if he felt this strongly, then he needed to explain to kids that he was seeing someone. She broke up with him the first time two weeks later, so talk never happened.
The point is, I was not good with kids meeting OW. Most advice suggests a minimum of one year. Hopefully h will be on board. My suggestion is if he brings it up, say that you understand she is a part of his life and that the children will have to be introduced one day etc. but it is early on for THEM.
I always validated Hs feelings about his GF even though I was absolutely certain it would not last at all. They are his feelings after all, not mine
My other point is that they will often like to remind you how serious their relationship is and how they really want to make it work etc. as I have been reminded a few times, believe none of what you hear....
Become happy. Drives spouses crazy. Simply because you are the root of all evil and OP is amazing. I say become happy because often the spouse thinks he will be happy when he gets away. Most times this doesn't happen at all.
Good luck, stop obsessing about the moving in, been there, done that. Doesn't help