[Oblarg]

This is likely a static friction problem, and the easiest solution I've found to deal with it is to implement a "minimum output" parameter that roughly corresponds to the smallest motor voltage which will result in actual movement. Then, you change your PID response so that the magnitude of the output is never less than that value, e.g. you can just add the value (with the proper sign) to any output, or you can simply set any output that is too small to the minimum value (again, with the proper sign). I think the former behaves somewhat better, but both work.

You can also implement cascading control, where the output of your angle PID is fed to a velocity PID for the wheels instead of directly to the motors. Thus, the internal PID loop will account for the problem automatically (provided it is tuned correctly).

You also really should not need an I or D term for a turn-to-angle loop.