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I am sorry to hear about this situation. Unfortunately, no. Unless you had a contract which specified that you can "void" the contract within a certain amount of time, this was a gift from one party to another. As such, it was FINAL. There is no "right" to take back the item (the dog is considered an "item" when it comes to things like this).
Someone in your situation can try to claim that the dog was only given temporarily and seek the dog back in small claims court. However as you have already stated that this was a gift, this would be a lie. Lying to the court can carry penalties.
You can try arguing that the gift was not final, and was premised on the fact that if you could secure the dog to stay there, the gift would be voided. But if so, you would have to prove this by a preponderance of the evidence.
In short, it would be up to the Judge, and what and whom they believe - whether this was a FINAL GIFT, a TEMPORARY LOAN, or a GIFT WITH CONTINGENCY, etc.
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