And then again, you may never see what you want to see in your nephew. But it doesn't matter.
No one can force anyone else to appreciate anything, whether it's what someone does for them...or how good oysters taste.
You either get it or you don't.
Being a parent isn't about recognition from the child or anyone else. You do it because you want to and you love the child. That has to be it's own reward.
With kids from divorce there are so many factors influencing them. #1 gran has been a stepkid for 3 of the nearly 6 yrs since the divorce. Right now she's going through a phase that I think is influenced by her divorced kid friends. For the longest time she didn't care much about seeing her father (or him her). Now, she HAS to see him because 'it's his weekend'. Ugh. It tears me apart to listen to her call him 'dad' not to mention be protective of what he does and why. All I can do is wait and hope and pray that someday she'll realize the truth about him and recognize that her grandfather and stepdad are the men who really fathered her.
I'm betting it's not your nephew's lack of appreciation so much as it's your own residual disdain for his father that's really getting your goat. Easy to recognize cause I do it myself.