You need to do a summation of torques. Using the side of your bumper/robot that you flipped over as an axis of rotation, figure out how much torque the robot provides on the right trying to flip the robot over, then figure out how much torque is holding the robot down on the flipped side. Subtracting the robot's torque from the flipped side's torque will give you how much torque there is holding the robot down. Then, you can figure out how hard you need to push to flip the robot back rightside up.
Of course, this'll only be a close estimate still, since as the robot rotates back to the upright position (or depending on how far it flipped over) your component of the force of gravity pushing down on your robot will increase and decrease as the angle changes relative to the ground, since as the robot rotates upright more of the force of gravity will be counteracted by the wheels on your robot.
My question is... wouldn't it be better to design the robot NOT to flip easily?
Then again, I think you may be on to something this year... I'm thinknig there's going to be a lot of robots crashing into those operator stations as people try to take those turns too fast.
*makes mental note to definitely add accelerometer G-limiter software into teleoperated control loop*
-q