I know some are saying that telling the kid not to even touch the horse was a bit over the top, but look at it this way. The young girl is brushing the horse. Said horse is not happy about a particular spot that is being groomed and the horse either spins and kicks her or turns and bites her because she can not move out of the way fast enough. Now her parents want to sue because she was hurt.
I'm a plus sized rider and there are days that I am a bit slower than I would like to be, but I am also an adult who has been around horses for 38 years so I am pretty good at reading them and can avoid an issue. She would not be able to do that.
Or everything goes well with the grooming and said girl starts to feel that the horse is hers and she can go over to see the horse when ever she wants.
I don't think you were wrong and your sister will just have to suck it up and deal with it. The horse isn't hers to offer rides on.