Why couldn't Leslie's dad give up the dog?
P.T. was Leslie's dog, and I'm sure whenever her dad sees him he remembers her in a happy way; pictures her with the dog jumping about at her heels. P.T. is a little bit of her that she left behind, full of life, funny, spirited - and for that reason, Leslie's dad can't seem to give him up.
The dog is all her father has left of Leslie. While he may want to give it up in order to comfort the boy, he can not do so because his own pain is so great and he recognizes that the dog will help lessen the pain for him.