Don't see why Tsunade should teach Sakura. Never saw her trying to heal anyone, unless yelling Saske-kun is a therapeutic jutsu that I don't know of...
She should teach Hinata. She always has her medicine with her and is always ready to help others... And since almost everybody in that damn village has been told to help Sasky, and Hinata couldn't care less about him, it would be good to have one person to care about the *rest* of the Konoha people.