Killing your companion animal yourself is not legal or humane. Unless you are a veterinarian, I think there is a reasonable chance that you could be charged with cruelty to animals if you kill your dogs. The current law restricts who can euthanize animals and prohibits many methods of killing animals, such as decompression chambers, curariform drugs, gunshot (unless the animal cannot otherwise be aided), and gas from engine exhaust systems. In October 2010, the law becomes even more specific and requires euthanasia only by injection of sodium pentobarbital administered by licensed veterinarians and other licensed technicians. SPCA agents, dog control officers, and the police can also euthanize animals under limited circumstances and only in the manner prescribed under the law, with the exception that gunshot is permissible as an emergency measure where the use of a humane method as prescribed under the law is impossible or where the animal is severely injured and suffering and cannot otherwise be aided. I suggest when the time comes, you take your animals to a veterinarian.

You should review your written adoption agreement, if you have one. An adoption agreement is a contract. Check to see if you agreed to have the agency bring the cats to a particular veterinarian for vaccines and under what conditions the agency can remove the cats from you. If you did not agree (in writing or verbally) to the agency bringing the cats to the veterinarian of its choosing, then the agency would have no right to enforce this condition. Of course, verbal agreements are difficult to enforce in court because oftentimes the two parties have different versions of the agreement.