Troubles in Gymnastics Class

Urg, I am having a rough time with my favorite 3 year old. I feel so helpless sometimes, trying to figure out what to do when he acts out.

He started a "big kid" gymnastics class last month. Instead of me being in the class with him, I sit on the bleachers and observe. The first class went so well! Here he is with one of his coaches on the balance beam:

It's been downhill since that class. He's been throwing tantrums, picking up items and throwing them and kids, and hitting other children! The worst part is, when he does it, he looks right at me. I know he's testing to see what happens. Although I want the coaches to be in charge, I also don't want to make them figure out what to do with a child who is hitting other kids. When he hits or throws things, I intervene and put him in time out. That causes him to cry, and then he is a helpless case for his coaches the rest of class. He's had four classes now, and we've left two of them within the first ten minutes because he just breaks down, throws a tantrum, and throws things at other kids. I'm trying to be consistent: If he is going to act out and throw things, then he gets a time out. If he keeps it up, then we have to leave. He loves gymnastics class (we'd done the parent-tot one for a while), and cries the whole way home because "he lost it." Yet, as soon as we get back to this class, he's up to the same behavior. I keep telling myself my consistency will pay off, but I'm disheartened.

Today was his fourth class, and it went a little bit better. He wouldn't listen to the coaches in the beginning, but he wasn't throwing a tantrum or trying to hurt others, either. He got to do the obstacle courses and had a great time. Then, he got scared in one of the courses. They wanted the kids to walk backwards on the balance beam. Rather than trying it or just saying no, he went berserk. The coach was able to take control of the situation, but Oliver started acting out every time the smallest thing happened. By the end of class, he was throwing things at kids again, and we had to leave.

One of the coaches stopped me on the way out. Of the two coaches, she's the "strict" one, but Oliver does better with her. I like her a lot. Anyway, she asked me if he was signed up for the next session. My heart seized, and I realized she was going to ask me not to bring him back. Only... she didn't. She told me he did a lot better this class, and she wants to continue working with him. She said she's glad he's signed up for the next session, and they're going to continue "working through some things."

I remember how challenging Oliver's old music class was in the beginning. All the other little kids would play, and he would just cry and want to be held. It took him months to fully adjust, but then he loved it. We were both sad when that class came to an end. I keep telling myself to be patient and consistent. Yet, it's so hard going back just to watch my kid act like a terror to the others. I cried on the way home because I just don't know what to do. I don't know if I'm being too strict or not strict enough. Right now, I guess my plan is to just keep at it, one foot in front of the other. Eventually, he'll figure it out. Right?