Maybe when she's doing something that's not good, you could just casually look over And be like "hey make sure you don't do that, he has a strange personality" or something like that to not make it sound rude.
I've had almost this same exact problem!(except the girl was doing it at a show and she was about 9-10 years old) I just walked up to her after she was yelling and walking all behind him and said "Hi sweetie, could you please not walk behind him or be so loud? He's not always a very kind horse and I don't want you or anyone else to get hurt." She smiled and said okay and then walked away and problem was solved. Not sure how old the girl is who rides with you, but I hope this helps! :)