You are correct that it doesn’t matter either way. Based on this being your second bomb IMO you have a WAW on your hands who must likely has been planning this for awhile. If she’s told her family there is likely no turning back right now. Doesn’t mean you can’t reconcile down the road though I doubt you will want to by then. IMO you should agree to the cohabitation and try to negotiate the best deal for yourself and son. The longer this goes on the more she will talk to other people and likely try to get more. Have you spoken to a lawyer? If not you should immediately. If you want to save the marriage your best bet is to lean into the separation/divorce and act like you can’t wait to be single again. Most LBS don’t have to ability to pull this off which is why the majority of the stories here end up in divorce.