The hardest thing for the ladies is to keep them going straight and not bail too early. Facing the pitcher, put a flat base the "rubber type" or something like that, even if you draw an "X" in the dirt at the front rt. corner of the box. Make sure they don't step on it as they are going forward. If they do step on it, they will never get the outside part of the plate. Getting to first faster doesn't help if you don't make contact. Since I've read that technique in a book, it's always been a reminder for my slapping DD's and it has helped them stay focused.
Crossover, no crossover is more a timing thing and those that can master it, great, if not to each their own. But you have to go straight and a good catcher will pick up on it if you bail.