I think horse, dominance, which a poor description, communication is subtle, it's based on knowledge and trust, but their whole body communicates, from a rested leg to a flicked ear, and often we are communicating like someone shouting very loudly in a foreign language, expecting someone else who does not speak that language to understand.
The horse vocabulary does include biting and kicking, while ours hopefully does not, but most of the time, where they stand, how they stand and facial expressions work day to day, but we ask them to do things, like stand in a moving box, in the dark and accept it, without sometimes clear where the benefit is. If you have children you often see a pony 'trying it on', it's not being naughty, but really it would rather wander off and eat grass, than be with a small person, it does not really value that much. in any terms it sees a valuable, as worth paying attention to. If the small person is backed by an adult presence, and will not run off crying, it will probably comply.
We had a pony that used to bully children. You could stand at his head the child one side, the adult the other side, if the child held the rope, he would headbutt them and push them over, you could pass the rope to the adult and he would not move. You can not make any horse doing anything by violence, all you do is make it more advantageous to do as asked, and negative behaviour not rewarded. The same pony would drag a child away from the ramp when loading, he would load for and adult, putting another pony in first and he would drag the child up the ramp, the advantage of being with his friend outweighed the child asking him something he wouldn't normally want to do.
Horses do a lot worse to each other than the odd kick, there is usually an escalation of events, even if we do not see it before it happens, and in horse terms is makes absolute sense. Horses are a lot more aware of our body language than we are, and the horse being kicked by the women was probably well aware it was in trouble long before she got anywhere near it, and if it was really frightened, or literally the grass was greener, it would have been off like the clappers. She lost her temper, which is human, the horse reacted in a horse way, it thought it better go in the box.