You can ask, but they don't have to do what you want. You agreed to watch the dog, and you volunteered to pay the vet bills, groomer, etc.--you could have refused. Having voluntarily done these things, you do not have a legal right to compensation for them--it would be different had there been an agreement in place under which you would be compensated or reimbursed; if there had been, you could sue (such as in small claims court) to enforce the agreement.The dog is their dog, and they have the right to sell it or give it away, or do anything else inherently legal with it. You of course could ask that they give or sell the dog to you, if you want it--for example, you could say to them, "if you give me the dog, we'll call it even on the money I spent on it."