There was a thread on here recently regarding a very similar situation and I was one of the poster who strongly advised the OP to rehome the dog. She clearly didn't want it, hadn't planned for a dog, her family life was really unsuitable for a dog and more importantly, she clearly felt overwhelmed by the whole situation.
However, you sound as if you would really rather like to keep this dog. And whilst working full time does make it difficult, there are ways around that. Could you afford a dog walker or doggy day care? Or is there any possibility of your dad having him for a few hours during the day once he's out of hospital?
I'm very much not in favour of leaving dogs for hours on end but a lot of people who work full time have dogs and somehow they must manage to work it out and this little chap needs a home.
It does sound like the poor little thing didn't have the best start in life. If your dad was able to just take him on without any checks on where the dog was going it sounds like someone just wanted to get rid of him.
If you're prepared for the level of commitment a dog requires, and it is a huge commitment if you do it properly, and you can work something out so he isn't left too long on his own, there's no reason why it can't work.
You have no idea what'll happen to him if he goes back to the shelter. You sound like a kind person and you've clearly already got rather fond of him, so yes, go for it.