Yes, I do my turns pretty much as you are saying, I turn my horse into my inside leg pressure and then if I have to I push her from the outside to keep her moving.
We used to have a beautiful side pass and could do lovely diaognal trotting (don't know what's that called in dressage, but we'd keep her body straight but her legs would be pushing her diagnally across the ring?). Now she isn't so responsive to my cues. We have a lot of make up work to do, and heck, if she never gets it, so what. We are just doing this for fun anyway :)