Probably depends on the judge. In my case we could use stuff for rebutal. So, if she didn't admit something.
I totally agree with hoosier_dad on timing.
Consider retiring, moving back with the kids for a few months. Or bring them to California with you.
Moving back and pretending may be a good choice and put you in a better custody situation. The stress may be bad, but it could also run her off.
Note: check your state laws. In some states (typically at fault states) sleeping with her after you have knowledge is consent.
Divorce is a declaration of independence.
It is easier to become a dad than to be one.