I was married for 5 years to the mother. After we married the father stopped paying court ordered support. I repeatedly asked her to report him to the local child support service. This is in California. She never reported it. She was worried what the other daughter would be brought into it by the father. We have recently separated and are getting divorced, do I have the right to sue the biological father for the child support he didn`t pay during our marriage?

No you can't sue him for back child support. That belongs to the mother. But you can sue him for losses you incurred because he didn't pay.