just my opinion...
As with any dog, you bring it home, and it is the most perfect dog...for a few days. Then the bad habits come out. How can this woman say that your dog is perfect with them. She can't tell that in just one day. Give it time, and they too will see the chewing/barking that you did. And who is to say that they will be as patient with him as you were. We saw your posts, we know how devistated you were when he went missing. I think that if you did leave him there, you would regret it. You would constantly be wondering how he was being treated...etc.
I think that that woman would do anything, say anything to convince you to let her keep that puppy. The kids may be sad, but that unfortunantly is a lesson that every kid needs to learn sometime in life. She as a mother should have made very certain that they understood, the second they found him, that he more than likely had a loving home, and wouldn't be staying. If she is that concerned about their happiness, she will take them to get a dog, and let them pick it out. As soon as they do, they will be over the loss of your dog. That dog belongs with you, your family, including your other dog. TAKE HIM HOME!!!