Trailbraker

The "diff rocking under power" is most likely you spinning your wheels and the ASR coming on (lights flashin on dash).

Its actually quite difficult to spin the wheels normally so I would suggest maybe checking you aren't being too sudden with the throttle..
e.g. Stamping on the throttle out of corners is a no-no for any FWD car.

If you really think you are being smooth and quick then switch off the ASR by all means, but its a generally a reasonable good indicator that you are being a bit eager with the throttle.

..Although on bumpy roads it can be easy enough to trigger it.

I'm not a doctor - but I really do recommend braking later