What lens to rent for dolomites alps trip?

So next month I'm taking a two week vacation to the italian alps in the dolomites. I will be in the mountains for about 10 days then will spend the remaining days in Venice before coming home. I have a Nikon D5000 with the kit lens which is quite a good lens for what it is. It takes very nice crisp pictures that do not require a big zoom. I want to rent one more lens to bring along for some different types of photos especially when i'm in the mountains. Should i rent the 18-200 vr or the 10-24 wide angle lens. I'm not sure which i will get more use out of. The 18-200 will be nice for its zoom to get pictures of something in detail. But the idea of a nice wide angle lens sounds great also so i can capture nice landscape pictures of the amazing alps. Any ideas or other lens you can recommend would be great. Give me your opinions on what i should do.

Added (1). Oh and if anyone has any experience with a trip like this, give me some insiders hints on some great things to do.

Added (2). Oh another point, i'm a very novice photographer. This is my first camera so the easier route is the better. I keep hearing about this stitching? What is that?

Added (3). I thought about a tripod, but i want to keep my pack as light as possible, and we will be on the move often. Alot of climbing and hiking.

Added (4). And there isn't much wild life in the alps I have heard.

PErsonally I'd stich. At 10mm you get all sorts of unwanted things in your pictures.

I'm a wildlife guy so I'd bring at least a 70-300. Alternative would be a 55-200 for some detail shots.

Also, bring a tripod. Seriously consider getting some and grads, cokin p-series for example. Do bring a polarizer.

I've been to the dolomites so I know sort of what you will need. Forget a telephoto lens, if you have the time (which you should, its amazing there) you'll find it much better to get closer to objects of interest than photographing them from afar. My recommendation is to rent something with the zoom range of around 16-35mm. I know canon has a lens like this. Not sure about nikon. If you can't find one, get a 17-50mm f/2.8.

In addition a 50mm prime lens (f/1.8 or less) will help with some shots and a macro lens can also help. If your really hardcore and want to bring even more, a 300mm prime lens will help, but you really don't need it.

Ok, so apart from the lens these are also VERY important:
-You'll need to be ready to hike all day, don't miss out the evening, sunsets are always good for landscape (bring tripod).
-Ask locals for the most photogenic hiking routes.
-Learn panoramic photography before you go! A lot of the scenery is captured very well with a 360 degree view.