Custody of children after divorce and purdah with step siblings

I am divorced with two children (boy 9, daughter 7). My ex wife, has as I am led to believe, settled down perhaps made or not made nikah with the man I accused her with whilst we were married. I am not sure but I assume he is also divorced, he too has two kids of his own, also a daughter and a son I think maybe a year older than each of mine.

My first question is: What is the most authentic ruling regarding custody of children post divorce? Where and with whom and from what age should they reside with either mum or dad purely from what Shariah explains?

My second question and this is what haunts me: If tomorrow they all decide to move in together and lets say they are indeed married for purposes of this question, how does the mahram thing work? This man, is he mahram for my daughter firstly. Secondly, his children being exposed to my children, I fear abuse, bullying, sexual abuse(possibly! as a parent this thought lingers as they grow older and left alone), and my children being teased by his kids - that they only in that home because my ex wife married their father. Tomorrow if these step brothers or sisters or whatever they will be termed, if their natural father purchases or does something for my kids , they could get jealous or nasty towards my kids, maaf but all of these scenarios seem to be playing out, hence my questions.