I'll get crucified for this....but he is not your dog. I understand he's better off with you, but he is not yours.
That being said...she obviously has "forgotten" how much work he is/was...she probably has given no consideration what expense will be incurred moving to NYC either.
I personally wouldn't agree to watch him any additional time. I'd tell her no to that idea.
You have the money together to pay her correct? Were it me...I'd flash that money in her direction...cause I'm betting she'd take it.
Hope it works out in your favor.
PS and get a receipt.