.22 sounds perfect. Recoil is next to nonexistent, so she wont get scared off and not want to shoot anymore. Shell also hit the target a lot more, and not get discouraged, and she will be able to work on accuracy and proper technique.
After she gets used to it, id let her try your 9mm. I wish my parents wanted to go shooting with me. That would be awesome. They pretty much hate guns, and want nothing to do with them, so that sucks.