Dogs bite. Why is this so difficult to understand? Humans bite, hit, etc. "We" know better. It just makes me mad at humans that make this the breaking point.

I understand you not being in a position to take this dog. Is there another local rescue in the area you could call? Could the family re-home the dog themselves?

Now, on to the contracts not meaning anything issue...lest we all get the idea we can just do what we want, without thinking of the documents we sign. I wanted to add this input...you are entitled to break a contract.
There are two issues- the first- what happens when you break a contract. The 'punishment' is what are known as damages. What damage happened to the other party when you broke the contract. Easy example. You sign a lease for 12 months to rent your apartment. You break the lease 6 months into it. The landlord has been damaged 6 months of rent. She/he can collect it from you (there is a duty on their part to re-rent....but, this is just an example). If you broke the contract with the rescue people....what are they damaged, really? Nothing. I suppose they could sue you, but, I don't see what they would recover from you. So, you don't end up with any real consequence. Like moving out of the apartment early, but, having already paid the rent. You are 'obligated' to stay there (loosely speaking), but, what is the damage caused by moving early? No damage.

The second part is- is the 'contract' really a contract. For a contract to be enforceable, there has to be a bargained for exchange. You gave X to get Y. I don't really see what your promise to return the dog to them got you. They didn't make a reciprocal promise. So, prolly, the contract itself isn't even enforceable. And, if there isn't a contract that is enforceable, you don't need to worry about what happens when you break it.

Just some basic info on contract law...now, on with the disclaimer..you can't sue me, I am not your attorney. You shouldn't rely on my advice, you should seek advice from a comptetent attorney in your area, blah, blah.