I am curious how the relationships between the WS and children are affected by them leaving for the OP.
My situation is different from yours as our children are adults with families of their own. During our separation, my exWH left me to live with his AP. And during the three months of living with her, he felt and saw the damage his actions brought on our adult kids.
Our oldest son refused him access to his children, refused to see him. He was disgusted, full of venom towards his father....I will add for context, that their relationship was not a loving one, just amicable.
My middle son accepted the situation and was totally mixed up as to his feelings, like torn between loving him and loving me. He shut down his feelings all together, kept contact with his father on an impersonal note. They would go to lunches together in a restaurant but the talk was just about the stuff not feelings.
My daughter was the most vocal with pointed questions for me and for her father.
She was the one who persuaded me to find a therapist immediately and did not want to see her father at all. Living in another town, she had the physical distance working for her.
They told our older grandkids at the time of separation, that their grandfather made grandma cry, that is why they separated.
They never met the OP. I found out later that my husband never thought about when or how to introduce her to our kids and our grandkids. He never introduced her to our mutual friends either. Never told them about our situation. I told only one close couple about his affair and our separation.
Our kids did know that she was wealthy, had lots of money, owned her big home, travelled lots, a widow of 35 years who never had children, a retired government director. I think my husband must of told them something about her...he sure told me stuff about her on D-Day. Like how exciting, sexy, interesting she is. On and on. I was devastated even as I knew that our marriage was shitty in the years prior to his infidelity. I never thought he would cheat.
Three years later , we have reunited. Our lives today are quiet, uneventful, boring at times thanks to the covid restrictions we have to live by. But we work at keeping up our morale and find things to do differently and look for ways to be likeable, loveable to one another. It's hard for me at times...and I know now that there are two choices for me to make every day: stay or leave. I have an exit plan, and to echo the writings for others on SI..he is not allowed to hurt me ever again. He is not allowed to hurt our children ever again.
But the toll it took on our children is heavy. I don't believe for one moment that adult kids are not devastated by one parent's betrayal and moving in with the OP. Their feelings of mistrust run deep. They even question my sanity for reuniting. But that is another topic altogether. All three are talking to their dad. And I notice the absence of feelings...like I love you dad or you are a good dad...that is gone. What I hear is thank you dad for babysitting, thank you dad for the supper you made. He is doing acts of contrition but what he gets is politeness and superficial talk. It's almost as if they have shut down parts of themselves so as not get hurt again. Their dad has difficulty in saying I love you to them also. I see there is a lot of work for him to do to regain their respect. To his credit, he did write an apology letter to them. But it seems that is not enough for our children.
I know that on SI the purpose is surviving as a BS and WS. And I'm glad that there are threads about infidelity and moving in with the OP, and its influence on children. This is my story, thank you for letting me contribute and share.