A breach of contract to a material provision of the contract generally renders it unenforceable in the Commonwealth of Virginia. Often, parties to a contract will attempt to find an act where the other party "breached first" and thus allowed them to discontinue the contract.
Has the will been adjudicated such that you are the title holder to the dog? Without title, I think that you have a difficult situation. Counsel gave good advice about title.
In the Commonwealth of Virginia, you may consider a partition suit for personal property. In this suit, you would offer to divide the dog, unlikely; sell your share to them; buy their share from them after allowing for costs in upkeep and maintenance of the property; or sell the dog with the appropriate accounting as mentioned. I am not sure that Small Claims Court may allow this sort of claim but it may. I am not sure how valuable the dog may be and that may drive some considerations.
You should consult counsel about the written contract and title to the dog and for specific information about your circumstances.
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Breach of a contract does not in itself Void the contract. However, the contract can be enforced such that if one of parties did not live up to their part of the bargain, a Judge can make things right. You may want to consider pursuing an action in Small Claims Court.
I said the following in response to your other question (edited for new information):
The first owner could only give you the amount of ownership she had, which is half. She could not give you full ownership of the dog.
Send the co-owners a letter, with delivery confirmation, and ask that they give you their half ownership in exchange for half the money you have spent in caring for the dog (vet, food, etc) as well as half of the daily boarding fee ($25 - 35 per day) for the amount of time the dog has been with you. Tell them if they do not agree, you will sue them for the money you have spent and for the daily boarding fee. Make sure you have firm figures of what you have spent. You should speak with a local attorney regarding wording.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.