Custody Battle Over Cats In Califronia

I know this seems silly. I just had to call the cops on my boyfriend for domestic violence. We are definitely breaking up and seeking the home we own together.

We have two cats together that we both absolutely adore, and they both love us pretty equally. We raised them from kittens however when we found them we did not live together, so about 80% of the time they were at his house. It was much bigger and had a nice outdoor deck that they could roam. I stayed over there often as my office was closer to his house, during this time we still split all expenses for the cats (food, litter, vet, toys, etc.) 50/50. I still fed them, cleaned their litter box and took care of them a lot. We bought a place 1.5 years ago and we still both take care of them and split all expenses 50/50. The pet insurance, food, litter & litter boxes were and still are purchased by me (he pays me later for his half). We really do split all responsibilities and they really do love us equally.

My boyfriend is very stubborn and there’s no way he will just give me the cats. Splitting them up is not an option as a they are brothers and have been a bonded pair since they were young (they are 3 now). We both work from home and can give them a good life, I just don’t want to lose them and I do have a fear that my boyfriend could be physically violent with them. He never has been, but given that he abused me it’s just my fear that has been developing.

Who would likely win this case? Is it even worth going to court over? Is it gonna cost me an arm and a leg?