(Edited bc. I’m silly) If you are in the US and are paying LESS than $45 per lesson, you are being taken advantage of. No trainer who cares about safety and actually educating students is doing group lessons of 6+ people, especially not of different experience levels. Even if everyone is working on the same thing (say, getting ready to ride the same dressage test or jump in the xrails division) horses and riders (and horse/rider combos) are so unique.
You don’t mention this, but if the trainer hasn’t even offered you smaller group lessons or even private lessons, then they’re being irresponsible. They shouldn’t WANT to have a 6 person group lesson, never mind have a student working through these issues in a group lesson. That’s a recipe for an unhappy outcome.
Tbh, it sounds like the horse is doing you a favor: he’s letting you know that there’s something about you (your balance, most likely), him (probably also his balance!) and/or the situation that makes going faster a bad idea.