WOW! that sucks...
could you take a test kit or some strips with you to check the levels...( or grab a sample for a free pool store testing)
I bet it's way off balance.

I'd also poke around to see what chemicals they are using... ( maybe they bought into the "copper keeps your pool clean" b.s.)

I don't know if there is anything that you could protect your kids with...
super duper waterproof sunscreen might help create a barrier
It may also be time to take them for a check-up @ the doctor... if they've been exposed to high contamenants

In the mean time, I'd give the kids some tylenol for any pain & possibly allergy stuff if you think they are having allergic reactions

Good Luck & I hope the kids feel better soon