That is cruel and unusual punishment of anyone let alone an adult who’s been off a horse for more than 2 weeks 
Can you ask for a longe lesson with the horse in properly adjusted side reins? That should reduce the bounciness and allow you to trot.
Failing that, find somewhere else with school ponies who are made for the job. It’s a thing - my horse would fail out of a school pony career in 2 lessons or fewer because if you don’t have ALL the skills, she’s going to bounce you right out of the tack and laugh at you while she’s doing it. That might be barely productive for an intermediate rider you’re trying to push to the next level, but absolutely counterproductive and possibly dangerous for someone who’s not been riding for a while.
ETA - muscles shaking are telling you that you are relying WAY to much on muscles and they are TIRED and beyond the point of learning. This is not your fault. This is because there is not enough forward movement in the walk and not enough lift to help you use your balance instead of sheer muscle power.