Do I really need a lens to cover in between 16 and 50mm?

I currently own Nikon D5100, a Tokina 11-16mm 2.8, and a Nikon 50mm AF-S 1.4G.

Do I really need a lens to cover the focal length in between these two? (17-49mm)

Only you can answer that for yourself, there are no rules in photography that say, "you MUST have lenses of this and that focal length."

Do you miss the ability to use those focal lengths? If yes, then you need one. If not, then you don't. It's that simple.

Depends, if you want a "normal" lens then yes. With the D5100, it has a crop factor of 1.5 which means that at 35mm you will be at what is considered normal (50MM). If you do alot of landscape photography I would think that you would want a lens to cover that range.Me personally, I think the two sharpest kit type lenses for the money are the 18-55VR or the 18-70. I have used many types of lenses and found that the 18-55VR is as good as it gets for the cost, it is my walk around lens at the moment.

Just my opinion, but I think the 11-16 is a great, sharp lens, but it is a bit wide for some situations. Again, what will determine what focal range you need is the type of shooting you do, which you do not say in your post.

To ask the question you have no idea what you need

so rather than consider a purchase in the near future forget about your problem and go out and shoot more pictures

Eventually you will find out whether or not something is missing and you can make a purchase then