This should not be construed as legal advice. I highly recommend seeking out a well-qualified lawyer. It sounds like you already have one but I would see if they have any experience dealing with the poly community.
This may be of some help
First off, you're in California. California sides with the mother in the overwhelming majority of cases and that goes up dramatically if the father is anything less than an ordained priest.
I would not recommend hiding your way of life because it says to a judge that you feel its wrong somehow and should be hidden.