Legal Question in Family Law in California

No. Who moves out doesn't have any significant impact on custody, which is based on the standard of: "best interests of the children." If you move out and set yourself up in a new place that will be a good home for the twins, it would probably be better for your chances for joint custody than staying in a deteriorating situation in the family home. Bear in mind that merely yelling alot, with children around, can be trumped up into a domestic violence charge, not for criminal prosecution but for custody purposes. So better to defuse the situation and then calmly persue your legal rights and remedies.