Using rudder to keep the nose up is called doing a knife edge. You use the elevator to keep the nose up during a turn - unless of course you're doing pylon turns.

Another use of cross-controlling would be for a side-slip. This is often seen done with Pre-WWII planes as they come in on final and wish to lose altitude without gaining airspeed, they will bank the wings in one direction and apply opposite rudder. This makes the plane crab, or fly sideways as it's coming in, which creates a LOT of drag and allows the plane to drop without gaining excess speed.

But for a classic, textbook turn, you bank with ailerons, hold the nose level with elevator, and combat adverse yaw with rudder - pretty much in that order.