This is an awful situation for you and Molly, and my heart breaks for you.
The only thing I can add is to ask how much you trust your vet and their opinion? The only reason for asking this is from a situation I was in a few years ago. I had a rescue Border Collie cross who had a split personality which was getting worse all the time. I'd had advice from behaviourist, those that would come out as I was refused by two because of the rescue home she came from. My vet, who was the practice owner, was also very helpful too as were some of his other vets.
I'd gone back again for more advice as she'd bitten me badly, and it had got to the point that she was biting me daily. I saw the vet who owned the practice who said that he thought we should think seriously about what we behaviour we thought was acceptable to live with but he urged us not to take her back to a rescue because she could not be safely rehomed and he especially feared for if she came in contact with a child. At the time I was really shocked as it came as it wasn't something that had ever even entered my head and I dismissed it immediately on the way home in the car when talking to my OH. That night she was flopped against my legs being stroke when she bit me again.
Thats when I began to think seriously about what the vet had said. The thing was that I trusted him totally, he'd been my vet for alot of years. However if it would have been one of the other vets who I didn't know that well that had suggested it then I really don't think that I'd have given it any consideration at all. That trust played a huge part in the decision to have her pts.
Despite how she was, I still found it devastating and was totally heartbroken but I do think, for her and us, it was the right decision.
Its a decision that none of us ever want to have to make and my heart goes out to you. Whatever you decide we're all here for you.