Sorry for your pain Miss Diva.This same thing happened to me when i found a tiny kitty on the highway...crouched against the median wall. I ran across 4 lanes of the expressway to retrieve her!! She was so cute and sweet! This was many years ago and we did not have the resources like the internet...if you lost a pet back then you put an ad in the newspaper. About 3 weeks later we finally found the owner, she came right away and picked her up. That lady was so happy to get her cat back! I was sad as i really wanted to keep that kitty!
(and i normally don't care much for cats...but this one was special!) I know it is hard but Molly is their dog so you must give her up. I don't think it is reasonable to ask if you can visit her, Would you want some stranger visiting you and your pet? That would be weird! It is just my opinion, but i think you should start looking for your very own yorkie to love! I missed if you got a reward or not, but if you did i would use that to start your own yorkie baby fund. That way Molly would kinda always be with you in some way! And if Molly was meant to be yours she will be! Keep your chin up! You did the right thing.
BYTW, the cat jumped out of the car window onto the highway on the way to the vets office!