Elites roll their shoulders on top of their controlled hip angle.
Sprinters keep their hips more flat and stable and roll more with the shoulders.
When I started swimming I read all those talk about power from the hips etc.
So i started rolling the hips like in the wrong example from the get hips with your hips video. It didnt work.
As far as I can see you are also rotating the hip, but not connected enough with the shoulders.
For beginners its best to start with just connecting the roll angles of shoulders and hips, to make the whole body rotate like one unit.
See from the 40 sec mark.
If you can lock the shoulders rotationwise to the hip action, then you can add some extra rotation of the shoulders on top of this hip rotation, but then its a controlled summation of forces, not an unconnected hip shoulder sloppy action.
Its good to first start with a feeling of rolling the body from side to side as a solid unit.