Again, you are thinking like an angry EX and not with good sense.

Your EX hasn't been living with her dad "for years". As per you, she only moved in with her dad when she left you about 3.5 months ago. So, was she living with YOU while taking pay under the table since you said she has been doing it for years? If so then how can you say it is wrong when she does it when she is living with her dad but not wrong when (if) she did it while living with you? If you are SO concerned about your D living with somebody that "defrauded the gov" then why are you only wiling to bring it up now that a custody issue is in place. In other words... if your EX came back to you or didn't fight you on custody it would probably be okay but now that you are fishing for something "bad" it becomes an issue.

Like I said... if you think it was wrong why did you NOT say something before now?