Can I Get a Stronger Battery For This Laptop?

Off the top of my head, no. You could get a portable booster battery, but it adds bulk and is impractical. I would recommend a Macbook of sorts. They are the choice of most students, and can perform all the tasks you require. For gaming, any laptop would be a disappointment. A proper desktop would be best for that.
 
I already built a desktop for 1500, I'm just looking for a good laptop for this price and no higher, only thing is the battery life is pretty bad.
 
2 hours while gaming. I assume that's bad, maybe not now that I think about it if you're gaming. I read that its hard to get 4 out of it while using office and such.
 
I wouldn't say that is bad. My laptop gets about 3 hours browsing the internet / light tasks.

It cannot game very well but when it is working hard I might get only an hour out of it.
 
Since you already have a desktop, i would suggest a nice small ultrabook. I still recommend a Macbook, so have a look at the Air. New version has 12hrs of battery life :)
 
If you want the perfect match for your situation, the $300 extra is worth it. Try find another ultrabook then. A normal laptop is not suited for what you want. that was the point i wanted to make...