I think William was parentified for a really young age.
The relationship between Charles and Diana was poor so William was expected to "take care" of Harry especially when they both were sent to boarding school aged 8. I cannot imagine what boarding school was like for William as he had to endure Tampongate when he was 11 and the Bashir interview when he was 13.
Diana used to use William as a confidante for her emotional turmoil (remember the reports of him pushing tissues under the bathroom door) and Charles seemed a bit like a distant grandparent/uncle. However this is Charles' failing and I think he lacks the emotional bandwidth to deal with Harry - probably because he had a strange childhood
I think things only got worse for William when Diana died and it seemed like it was convenient for William to deal with Harry and make him William's personal +1. In Spare it seems that Harry almost felt Kate was a wicked stepmother when William wanted to spend time with her. Even today the press seem to think that William should be responsible for Harry.
I'm interested to know what you mean by William "doing duties"? - he has carried out public duties since his teens, served in the military and done internships. The normal stuff for a royal
The problem was Harry - he was meant to have a longer army career I think but he flounced (see a pattern here) when the next career step was a desk job. So they hastily teamed him with W&C