With full body weight committed to the pushing leg (and the other
non-pushing leg lifted off the snow)
2 - Hips-rise-forward and Leg-recovery
3 - Double-Pole-push
4 - (optional) Glide
5 - Prepare
Just before the next leg-push, transfer full body weight to the next
pushing-leg, and actually lift the other leg up off the snow a little.
muscles
For sideways transfer of body weight:
hip adductor of pushing-leg, and/or
hip abductor of other leg
torso-rotators in the abdomen
The hip adductor / abductors more the hips and the weight of the
whole upper body sideways. The torso-rotators move only the weight
of the chest and shoulders and head. Either is good
Most people use the other leg to push their weight over sideways (by
pressing the outside of the ski against the outside of the track), but
it's slightly more optimal to use the pushing-leg to pull it over
(by pressing the inside of the ski against the inside of the track),
because that way the sideways distance is a little bit less -- but this
only matters for elite racers.