"What to do on the first three of a Natural Turn in the Waltz, This is how it was explained to me. If we stood feet together and stepped to the side on the toe and analyse what we were doing. I think you will agree that all of us would flex the standing knee to push to the side. We wouldn't need anybody to tell us to or how. Heres the rub. Put the first step in front of that step to the side and the flexing of the knee gets lost. In a nutshell we should drive that first step and also drive onto the second step at the end of the first. Two driving steps out of three. Do that correct and everthing else will fall into place. This came off an instruction tape by a very well known teacher. Good Luck"
Don, the critical difference which you are overlooking is that in an ordinary natural turn, although the second step ends sideways, it begins forwards, and thus the action is more forwards than sideways. Closed changes and 1/4 turn naturals use something closer to the sideways action you have described.