Decreasing sensitivity of my PS2 controlled bot

    Input1 = map(ps2x.Analog(PSS_LY), 0, 255, 2000, 1000);

What proof can you offer that the Analog() method returns a value in the range 0 to 255?

The other values are the speed to set the (continuous rotation, not really a) servo to. If you want the robot to go slower, use two values equally closer to 1500 as the to range.