Note that I am not licensed to practice in your state. This is not intended as legal advice. Please check with an attorney in your state
She needs to go file a police report for identity theft. If she does this, she can then take the police report to the credit card companies and also the 3 credit bureaus to dispute the charges and accounts and have them closed. This might also help her in her child custody and support case because it shows that he's dishonest and is willing to use the children for financial gain.