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I am so sorry for your troubles. California law does recognize palimony or as they are called in California "Marvin" claims. In a Palimony or Marvin Claim, a non-marital partner’s right to monetary support or property is dependent upon an expressed or implied contract, or some other fair and legal basis for the claim. In your case, you left your previous arrangement to come live with this gentlemen thinking he would take care of you so an implied agreement was created. You even had an oral agreement that he would support you. Furthermore, you would be entitled to child support if you are awarded custody. You should strongly consider engaging a family law attorney locally who can push this issue for you.
There is also a state agency that can at least help pursue child support should you choose to leave this individual. http://www.childsup.ca.gov/
Your options are not limited, you just need to be prepared to fight for your rights.
That is what I'm talking about. Because you cohabitated you are entitled to support or palimony as either a lump sum or monthly payments.
If you need a referral to a family law attorney, contact your local or state bar association and ask for a referral to a top family law attorney. They keep updated lists of attorneys in each practice area for referrals. You will likely be able to get him to pay your attorney costs as well because you do not have a means for support since you chose to stay at home and care for the kids.
I know these are tough things to deal with. I hope it all works out for you. If you could accept and rate the answer, then I can close it out.
Also, we do not get credit for answering until you accept the answer. Again, good luck to you.