I never trust a horse 100% simply because of the fact that horses are animals of prey. They will ALWAYS resort to inate instinct if it realy boils down to it. How well they are trained plays a HUGE role on a horses behavior and turstability. My late mare who I trusted 98 % of the time was a well behaved animal but a couple times she would have resorted back to instinctal behavior if I wasnt there to guide her. She was a steady mount and I trusted her with children as long as I was there and with them. After all she was a big horse and could be intimidating to the little ones due to her size. She was always very well behaved around children and rather gentle with them but she was still a horse. She was used as a trail horse for ppl to rent and ride at one time.
The level and completeness of training plays a huge role in building a great horse with alot of exposure to external stimuli. Many ppl forget the foundation training and then boo hoo that thier horse is unsafe or lacks good behavior. Of course if a good tempered horse is used consistantly through out the years they eventualy get used to thier surroundings and other stimuli thus making them more level headed in thier older ages. (However this is not always the case with some horses it depends on various other things as well.)
Sounds like you have just ran into a few that were not as they were described. You will run into that more often than not. That is why its best to be selective and pateint when looking for a good mount. You may want to take a experienced person with you to help you out on your selection. I knew a guy who stated that everything he had was "kid broke". I think he meant the horses will break your kids. Most of what he had I wouldnt ride myself let alone a child. With this guy....Buyer beware indeed.
Some horses are just full, high spirited and some are just natrualy high strung.........but and this is a big but.....they should still and can be well trained. I rode a Go go get em horse who was well into his teens that was not for children but WOW what a ride he was. He was great to ride, full of spirit and full of energy and would go any where and jump anything for you. Was honest and never offered to rear, buck or bolt but was just full of go. He was well trained, would stand still for you to mount and would stand still if you asked him, he would listen to your cues and perform with out much ado but he was just very forward and strong. I personaly loved him. He was a lesson horse for the higher level riders at the school I attended. On the ground he was great as well. So one can be high spirited and or fulll of vim and vigor but that does not mean they cannot be well trained and reined to use that energy for the better. High spirited does not and should not mean untrainable. I have ridden high strung Saddlebreds that where full of energy but well behaved and well trained under saddle. Its all about the trainer and some about the horse. Some horses just put up will the nutty things thier riders do regardless of thier level of training.......those make for even better horses to ride and trust with.
"The question is not, can they reason? nor, can they talk? but, can they suffer?" Jeremy Bentham