Is this with the parking brake on? Maybe driver's side rear brake is not activating when you pull the parking brake.
edit- You're not talking about the rear of the car? It's the front? Check the engine/trans mount, or subframe/cradle mount. Sounds like a broken mount.
edit- You're not talking about the rear of the car? It's the front? Check the engine/trans mount, or subframe/cradle mount. Sounds like a broken mount.