If the family law court orders me to attend Batterer Intervention Program, what is the affect on my immigration status?

You need to ask an immigration attorney. On common sense-- I;d attend!!! and I would clean up my act!!!!!

Modification

I agree with Rebecca, but I would add that I recommend that you seek some family therapy or parenting classes,and (at mediation--this WILL be...

Who gets the estate???

This question cannot be answered based on the information provided. IF the home was in joint tenancy AND the affidavit if death off joint tenant...

That depends on what the judgment says, but conflict between parents is always harmful to to the child(ren). Always, no matter how "wrong" one...