I think it's crazy that she (or anybody) would think that $50 a month is a reasonable SHARE of what it takes to feed & clothe and equip a teen. It's not like you're asking them to pay the transportation costs. And 8 weeks out of 52 is not a lot of time, but he turned down other time in the effort to help you save money on transportation. It seems that when he took on the burden of this new family (and adopting kids he can't afford) he went beyond what he can handle, but that shouldn't be your kids' problem.
When you moved there, it was with his blessing. Don't let him turn around NOW and make you feel guilty for keeping his kid from him. The fact that you have more of the kids' time means that you have more of the expenses.
BUT if you are OK with the stupid $50 a month, I see no problem with accepting it in a $600 per year increment. Having him "deposit" it all, so to speak, at the beginning of the year for you to use as you see fit that year.
I still think you should use the guideline scoresheet for your state to find out what the ballpark SHOULD be for his current income, your current income, etc. And I can't imagine the judges deciding to let him allow his natural kid to go hungry just because he allowed the kid to move to Florida and adopted 5 new ones. If they want to keep jurisdiction over your son, then they care enough to make sure your son is being taken care of, and if they would not do this, I'd be VERY surprised!