This has the potential to be a very dangerous and unfortunate situation. Quite honestly, the safest and most appropriate way to establish dominance in this case is for your son to be bigger than the horse and for him to naturally exert that dominance, not to try to make the horse understand.

This horse is doing what horses naturally do, and although it might be possible to do some dominance establishment exercises, etc., from a developmental standpoint, your son may not be ready to take on that role. He simply may not have the ability to read the horse and "put 2 and 2 together" yet, so to speak. It takes timing and finesse to fairly gain a horse's respect and that is a lot to ask of a three-year-old child (and many adults).

If it were my child and my horse, I would be the primary handler of the horse. I would model appropriate behaviors for my son, and I would never leave him alone with the horse until such time when he was fully capable of handling her safely. There are many books and videos on horse training that could provide tips on establishing dominance, but I would leave that to the adult, not the child, at this time.

It is also important to remember that, although miniature horses are small, and sometimes only as big as dogs, they are horses still and should be approached/treated as such. They look cute, but they still kick, bite, and strike, like any other horse.