Their threats are baseless. They have no authority to deport you or take your children. In any situation where you are victim of a crime, you should contact local law enforcement. It's the criminals who face deportation, not their victims.
California has a state office called: The Office of Privacy Protection. It contains much information which should guide you in how to proceed to report the crime. Here is one of the menu items which can get you started:
And Mr. Winter is correct: their threats are baseless. They are trying to intimidate you. I don't practice immigration law but I know that you can get some kind of long-term temporary immigration protection if you are a victim of domestic violence. I'm going to change the practice area to "Immigration" to see if there is any more advice for you from that angle.
Your hsband's acts are typicl of an abuser. Simply report the misuse not only to the authorities but also to the various credit agencies involved. You wiol need to do that or become "stuck" with the debt.
As to any family law actions [divorce] if you do not personally have the funds, see the family law facilitator [San Joaquin has one so I assume Alameda County does also]. You can as for temporary restraining orders to protect yourself. BUT if you are going to change any finances such as bank accounts, do so before you file.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.