C.G.
I agree with Christy!
Your child won't care one BIT as an adult who paid for what-but she WILL remember Who set the proper example and didn't try to "get one over on the government" or whomever...
You might want to check with your atty first (unless you can make heads/tails of the divorce/custody agreement).
If your custody agreement SAYS that HE pays ALL the childcare then don't pay him anything and if it says that you split it 50/50 then I'd have my atty send a letter to him that you will be paying YOUR 1/2 Directly to the day care.
I'd try and let an atty handle it ALL if possible b/c otherwise it could get unnecessarily ugly-sounds from your description that he wouldn't hesitate to use it against you in the future if it would benefit him.
I'd get w/ your atty and see what the C.A. actually Says about who's responsibility it is to write the checks for childcare and go from there. I'd also let the atty handle any correspondence as they would keep you out of it-well from direct contact anyway- and sounds like you've been through enough.
Good Luck,
C.