If it takes 90-120 days then I think you should be filing asap to get on the hearing schedule. Why wait and then have the delay. Your actions are about what you want. His actions are about what he wants. If you do not want a divorce, then I would not file for a divorce. If he wants to do that he can. I WOULD however IMMEDIATELY file to resolve the interim child custody and support.
I don't think you can read much into the monstering patterns. Mine was very nice to us the first few months of OW2. Now he is being distant and if there is any R discussion (and by that I mean me trying to get the separation contract out of him) he monsters. He was horrible the whole time with OW1. You are still looking at him too much, but then you already know that.
I would not go anywhere with him at this point.
I agree with your father, I don't think he would have walked out on you guys without the new woman waiting in the wings, especially given that it sounds like he still doesn't have a place to go much of the time.