sounds like the bike is either to small or not adjusted right. when i had my first bike, it was to small frame wise, and the seat tube was nearly out of the seat stay. I could not corner for crap, and my knee's would almost impact the bars. I exchanged for the larger frame, and i can cut corners doing 20 mph like nothing, and overall it's just much more controllable.

also lean into the turns, sheldon brown has a good article on this. You don't need to lean in like a pro motorcycle racer, but just slightly, makes a big difference.