I'm willing to bet that CA is a more favorable environment for you than nm but do talk to a pro. CA state law is very clear - having testicles while Caucasian is a serious matter....
Seriously though, very favorable environment for you.
Once ANY action is filed and the respondent notified you are almost certainly going to be subject to "Standing orders" - basically mutually preventing you from incurring debt, secreting assets, screwing with policies, harassing each other or the kids... Google your county, divorce, standing orders to see what's what.
If you are separated and he incurs liability for say, driving through a china shop, I don't know that you'd be protected unless a divorce was finalized, it's still community property. If your joint assets are substantial this is a great time to setup an educational trust for the kids, fund two IRA accounts etcetera.
Know where everything is - insurance policies with residual value etcetera.
If you are there you are there and my sincere condolences. Try to focus on making the kids feel secure... Watching a movie under a blanket with a pile of kids and pets doesn't make your troubles go away, it just makes right now a good moment and helps you keep straight what matters.
Hang in there. I hope he stays safe.