"Anonymous. Just as a matter of interest
and from somebody who knows nothing about physics. Are you saying that the swing of a pendulum will reach its maximum to our left. Whilst it's out there the pivotal point moves over the maximum swing of the pendulum to be repeated. In the Waltz it is one swing or two. It must be one."
Each time you reach a maximum of rise and start downwards, you begin a new swing, which will consist of the down and the following up. When you reach the maxmimum of rise and start down again, that will now be a new swing.
For waltz pendulum swing, each swing has a single fixed point about which it occurs. (At least in terms of the location of that point over the floor area, it's altitude might vary)
"And whilst we are swinging before the pivotal point arrives, we have sway."
You shouldn't. First, its probably not a good idea to try to literally connect sway and swing, because that will lead you to seeing the sway as being related to a pendulum swing, which it really is not.
But to correct the specific mistake - before you pass the pivot point of the swing, you are dancing the downswing. And downswings do not really have sway, except maybe a tiny bit right at the beginning which rapdily vanishes. Only the upswing - occuring after you pass under the pivot point of the swing - would have lasting sway.
"The book though says we have sway on step two and three."
The sway develops throughout step two, it is there at the beginning of step three but should usually vanish during step three so that there is none at the end.
"Which I believe gives us swing on two."
You have swing on three, one, and two. Then a new swing on the next three, one, two.
Imagine "dancing" with a small child you are pushing in a playground swing (though you would have to reverse direction on each peak of rise and go back the way you came)