For your comment that if there is enough proof she will get caught, well my ex has been working cash in hand for 3 years now. I gave CSA full details of company, exes run, etc and they will not pursue it.
You are lucky that you have the choice whether to accept CS or not. A lot of people do not have that luxury as it is how they can afford food or roof over their heads. I doubt you have trouble accepting money from your new husband for support of your kids though. I also doubt you are turning down any government benefits you would be eligible for.