I thought giving the puppy to his little friend in the orphanage was a VERY irresponsible thing to do. How the hell is he going to take care of it in the orphanage? I doubt the orphanage people will even allow pets. They'll probably take it away to an animal shelter. Ugh! Fred makes me angry.
It's a movie, let it go. No, a child in an orphanage probably wouldn't be able to keep a dog. Then again, if that child has Santa's brother as his mentor/unofficial guardian, I suppose it's possible. If that's the part you found the most unrealistic, I'm worried about you. Besides, when they show the scene of the kid with his new family, the dog is there, so he clearly didn't have to give it up.
"There isn't any more, you drank the whole fairy...and you're going to your room."
I'm sure Fred talked to the Orphanage the next day and could make arrangements. Could donate money he got from his brother to help take care of the dog until the kid found a family.