Your son's behaviour is very confusing. It seems that he is very unhappy about something in the aftercare program, structure, teacher, etc. Remember that at this age, even if he is very verbal, he is learning how to express his emotions, and, he may not be able to express deep discontent. I would talk to his teacher about the specific situations that trigger his misbehaviour, snacks, down time, outside play, etc, and work out a plan to change it.
I would definitely not go for a seat where he is strapped. As a matter of fact, that suggestion from the teacher just speaks volumes of her. She seems to be authoritarian, and in my own experience, that does not work with young children who are just learning to listen, and to follow instructions.
I was in the same situation a few months ago, where my 4 years old son would behave nicely in his other activities, and not well in a home school program, with other 3 kids, we had at homee. After terminating the home schooling, the problem ended. It turned out that he was very unhappy about his teacher, and the structure set up (the school was set up by the teacher more geared towards girls than for a boy play). The teacher was somewhat authoritarian, and not proactive at all, and, did not believe in redirecting the children when issues arose. He is doing really well at his new school.
I totally understand your frustration and impotency. I hope this whole situation is resolved soon.
D.