In a side slip you do have lateral movement reference the ground. The aircraft will move in the direction of the lowered wing, off setting the drift. That is why you lower the wing into the wind. Otherwise you could slip in either direction and it wouldn't matter.
This is incorrect as well, similar to Charlie Tango's thoughts. We need forget about "side" slip vs. forward slip. Slip is slip. Slipping does not cause the airplane's
flight path to
move sideways. It simply causes a misalignment in yaw attitude. Flight path does not change. Go mess around in no wind conditions and transition from coordinated flight to a slip and back - in both directions. The airplane doesn't start drifting left or right of your flight path during a slip. If it does, then you are doing a slipping
turn, not a constant flight path slip required when landing in a x-wind.
You could be tracking the runway, crabbed down final in a x-wind, and then put in a slip in either direction. You will still be tracking the runway, but in one direction the airplane will be aligned with the runway, and in the other direction, you will simply be more misaligned than you were during the crab in coordinated flight.
The bank angle during a slip is
not to move the airplane sideways into the wind. It's only to keep the airplane from turning in the direction of your slipped rudder input. We do not want the airplane to turn. All we are doing when going from a crab to a slip is misaligning the nose so that the landing will be smoother. Aileron is used to keep from turning. If you are drifting, it's not because you don't have enough aileron, it's because your
flight path is not sufficiently into the wind. Aileron would need to be used to
turn the airplane's flight path more into the wind, not create more "lateral movement". Once sufficiently turned into the wind, you use the amount of rudder required to align the airplane, along with sufficient aileron to keep the rudder input from
turning the airplane downwind.
So think about this - you are in your J-3 Cub gliding down final in zero wind - aligned with and tracking the runway. Now you put in a big slip. You are still tracking the runway, just as you were before the slip. So then, what exactly is your "lateral" speed through the air now? There is none. The airplane does not start moving to the left of the runway track unless you are turning.
It is physically impossible to move an airplane "laterally" through the air at a constant heading. It is only possible to turn the airplane, which causes your heading to change.