So your adoption contract says that your group has the right to check up on animals you’ve adopted out and that they must be returned to your group if they’re no longer wanted, right? And your foster agreement says the foster’s got to return your dogs to you. You’d think that would be enough, and in some jurisdictions, it is.
But it’s not a sure thing, not by any means. A lot of courts are going to treat your carefully-researched “adoption” as a sale of goods and are not going to enforce a post-sale provision. In legal terms, you don’t have “standing” to bring a lawsuit to recover your property.
The answer to the issue of standing is to have a trust. A trustee has standing to bring a legal action on behalf of a beneficiary. It will look a lot like the Pet Trust but will cover all the animals past, present and future in your rescue.