Some people will intentionally get jobs that pay under the table while other intentionally quit jobs shortly after getting them to stay a step ahead. Unfortunately, it doesn't matter the amount that's paid in comparison to what's owed and I've seen this first hand with my past coworkers. The father of her children (twins) owes at least $40,000 and hid like a criminal until they both turned 18. I doubt she'll ever get $1,000 of it, let alone more because he lives at and works at a cheap motel.
The laws vary and in too many cases you'll find the other parent actually refusing to cooperate with authorities when it come to getting the person locked up for non payment. I can think of at least two women off the top of my head whom I've worked with that refused to have the guy locked up while they got upset and stressed out because they couldn't pay for basics for their kids and constantly juggled bills and bill collectors.
I don't think that this system can be fixed in time enough to assist you. It will take an extreme amount of effort from inside and outside the courts as well as a lot of money lobbying politicians to change the laws to be more uniform. He is atrociously behind, I say do everything in your power to lock him up. When he gets out, he will have renewed fervor in taking care of the life he helped create.