I’ll give you a synopsis of what I’ve learned over a 3 year period trying to find “the” horse. And getting two greenies that were too much and one horse that sounds like yours - got pissed if pushed and responded by bucking.
If you’re not experienced and/or need a confidence builder I would suggest steering away from dealers. The dealers I’ve dealt with have been anywhere between completely honest to out and out liars. But the main things are: they have only had the horse a short time so don’t know its history, and they are experienced riders. Unless they have a beginner type person on site to ride the horses they sell they can’t possibly claim them to be beginner safe, child safe, bomb-proof, or any of the sort.
I decided for my last search (hopefully for a long while!) I’d concentrate ONLY on horses privately owned for several years with a known history. I decided to stop looking for height and age first and make temperament my #1 priority.
Also, it’s a LOT easier to train a lazy horse to move out than it is to get a ditzy horse to calm down - at least at the inexperienced level. Sure a trainer can train a horse very well, but in the end, YOU still have to get on and be sure the horse isn’t going to get silly on you because you’re not as confident or experienced as a trainer is. Just sayin’…
Good luck! There ARE great horses out there!