I learned something from an old co-worker of mine. I think it'll help in your situation.
You see, what the court basically doing is charging you to take care of your kids. So, play them at their own game. EVERYTHING is about paper trail. What my co-worker did was open an account that was only used for his three girls. When he got divorced, judge granted the wife the kids, cars, house and had him on both child & spousial support. He moved back to Florida into his parents home since he couldn't afford his own well being. So, he opened up a bank account that was used only for his girls. Doctor appointment, co-payment, he swiped, day care, he swiped, shopping, he swiped. And now you know with technology and all, for every transaction you can add a memo to it. So, he joins the reserves and got promoted quickly. At that point in time, he was more than $70k a year. He left this job to go active duty. Even while at this job, he was making over $40k annually. But the same amount he was paying from the start, which I believe was $500 or some change, continued to stay the same. Before he left, he actually mentioned how the child support payments decreased to about $280 a month. Whenever his ex-wife would go to court and demand more, seeing as he was continuing to make more, he would show up to court with statements. Paper trail. They saw that outside of his payments, he was diligently taking care of his children.
I would suggest doing what he did. It actually make sense. Keeping receipts isn't enough. They can always excuse that as you just withdrawing money but it not really being for them. Open a bank account just for your kids. Whatever activities you do, use that account to make purchases on them. Ask your bank how you can sticky note memos to every transaction (some banks- like mine- can be done even thru the mobile app.) After some time, months or even a year or so, go back to court and contest the amount and show the monthly statements as proof of what you're doing for your kids.
I hope this helps.