I'll weigh in on a few things:
1) CLS will not give you any more money than the Hamilton. Some chick had the gall to ask this in front of everyone at the Admitted Students Day, and the dean of fin aid said they don't provide anything on top of that.
2) I don't think it could hurt to send a copy of your Hamilton offer to H,Y - but don't expect anything from it. They don't offer merit aid, and their likely response will probably be that their offer is need-based and not subject to change barring a drastic change in your financial situation. Still, might as well try.
If I were you, I'd thank Yale for its very generous offer, accept the money at Yale, and never look back.