@utay62 At 2 years old your son may not be ready for an organized gymnastics class. There is no shame in that. Some kids can handle it and some can not. You handled it the right way by removing him from a situation he could not succeed in.
I don't yell or punish. We have rules and set limits. There are consequence for breaking those rules. As toddlers if they threw a toy then the toy was temporarily placed in timeout. If they hit or bit their sibling then they had to apologize and go get ice for their sibling. If didn't matter if ice was needed or not, but it allowed me to separate them, comfort the victim, and gave the hitter/biter a peace offering. As they got older we were able to keep the same style of parenting. If they stayed up too late after bedtime then the consequence was going to school tired the next day. If they put a hole in the wall after kicking a soccer ball in the house then they helped me patch up that hole. We sat with them, explained what rules were broken, talked to them about the consequences and/or how they could fix it. We also let them know any time they got a new freedom or responsibility (staying home by themselves, no more screen time limits, etc) it was because we trusted them but if they showed us that they couldn't handle it then we would have to step back in to help them until they were more responsible. That was a huge motivation to both of my kids. As a result we never had an issue with lying. They knew that was the easiest way to ruin trust and ruining trust meant less freedom. If they lied about brushing their teeth then that meant they needed supervision again until I could trust them to do it themselves. I'd say we mostly relied on natural or logical consequences to their actions, talked a lot, and highly valued trust/honesty.
My kids are older teens (19 and 17) and the teen years have been wonderful. They are great kids and neither have any behavioral issues. We avoided all of the issues I see parents talk about (sneaking out, drinking/smoking, drugs, bad grades or skipping school, etc). They are turning into great young adults and we have a very close relationship. If they messed up then they told us and we dealt with it.