These types of cases are what I call the "Liar, Liar, Pants on Fire" cases. They are difficult but "fun" to litigate, when you are able to catch the Liar-Liar.
California law allows you to impute earnings to the other parent if he or she has the ability and opportunity to earn income but chooses not to. California Law makes it clear that a parent's principal obligation is to support his or her children. If the other parent is able-bodied and qualified to work at McDonald's (or wherever), then he should pay some child support. If he is capable of earning more, then good for you and your children.
If you can show a financial connection between the girlfriend and the father of your children, you may be able to "join" her in the family law matter, and thereafter propound discovery to uncover the true financials of the both of them. You may want access to the business tax returns, bank statements, etc.
There are many options in these types of cases, but unfortunately, this is probably not a matter you can handle yourself. If you have the means, you would be well served by retaining an experienced family law attorney.
In sum, you absolutely should file a case for child support. Your children deserve to be supported by both their parents. Also, it helps that the other party is making what are called "admissions" about the stacks of cash he has. Good luck to you!
By answering this question, the Law Offices of Cathleen E. Norton does not intend to form an attorney-client relationship with the asking party. The answers posted on this website should not be construed as legal advice. The Law Offices of Cathleen E. Norton does not intend to make any representations about your family law matter, but rather, seeks to provide general information to the public about family-law related matters. You should consult with an attorney to discuss the specific facts of your case. Thank you.