Is there any chance you can not stay in the same house for awhile? When we were divorcing, granted very many years ago and we both are married now to other people, we didn’t stay in the same place. It helps to avoid conflicts. We had a peaceful divorce and remained friends, I think it helped not to be there all the time. I think. Don’t really remember details

Also even if you say that kids don’t know, they alwars feel something is up. And I know you said you don’t want lawyers, and it is a valid point but sometimes letting others to deal with minutiae of dividing assets etc is helpful. Helps you to keep your distance