Personally I think this is a bad idea regardless --

if he wants her to have a chance to grow more responsible:
then I think if he presents a contract to her it will instead continue their current dynamic ("it's all his fault"). The only way it could possibly work (IMO) would be to have HER input in drafting the agreement vs. his presenting one. This would necessitate them sitting down together and negotiating the terms (and possible future re-negotiation) which sounds very unlikely at this point.

if he just wants proof to show her why he refuses to give her money:
then I think the contract is not worth the time and effort because he already has plenty of valid proof of why, which she doesn't accept as valid proof -- this "proof" would be no different.

LL