My daughter gave me cash in exchange for me writing a check, now the stable is claiming I am responsible for all the bills because I wrote checks to them prior.

A stable as in boarding a horse or other livestock?

If your daughter signed up for the stable, then I would think the liability would be all hers. If you co-signed for the stable, that's a different story. Can we have more details about the situation please?

Off hand I don't see how the fact that you once wrote a check somehow obliges you to pay all your daughter's bills from that point onward. But more info is needed here. Is there a contract either between you and the stable or between your daughter and the stable? Did you ever agree with the stable owner either verbally or in writing to cover your daughter's bills? If this involves boarding a horse, who owns the horse? Oh, and how old is your daughter?

How old is the daughter ? If she is a minor a parent would be responsible,

If the daughter is a adult and they signed or made a verbal agreement, you sending in a payment for her does not make you liable at all.

... if she is a minor a parent would be responsible, ...
For necessities. Stable fees are not necessities.