I have actually never considered Kiaras hunting skils (or lack thereof) being a deliberate move on the writers part in order to bring Kiara and Kovu closer together. *is dense*

I think that Nala (perhaps also with the help of other excperienced lionesses from the pride) has taught Kiara how to hunt, and like it was mentioned, I have no doubt that Kiara is younger than Nala was in TLK. Plus, considering how Scar made the lionesses overhunt, one can assume that Nala gained more excperience quicker. I think Kiara would have done well if she had had more time to prepare/more training.
Regarding how Simba`s over-protectiveness comes into it, I imagine he would feel nervous about his daughter learning to hunt due to the risks involved, but I also hope that he actually stayed out of it for the most part, considering that it`s the lionesses who do the hunting, so it`s not like he`d be able to train her himself. (he grew up eating bugs anyway, he`s most likely never learned to hunt at all)
I do not think that Kiara would refuse to learn how to hunt, though. It is clear that she (as a cub, in any case) had reservations about becoming queen because of the immense responsibility, and being given a role she never asked for. I personally don`t think she would resist learning about hunting. She was very excited and seemed confident about her first hunt, I think she was looking forward to showing her parents (Simba) that she was capable of doing things on her own, and hunting would give her a sorely needed freedom and excperience of mastering a skill.