Tell him "look, this game isn't about being a Total Badass By Yourself. It's about working with your team and overcoming challenges you couldn't otherwise. If you wanna be a Total Badass By Yourself, there are games you can play. But if you wanna play this, you're gonna have to work with me here. Because my time and effort is valuable, and I want to have fun just like you do.

The fact your seeking feedback suggests no, but it was certainly a bad move, both as a DM and as an uncle. Punishing anyone, though especially children, without explaining why is mean. You have a responsibility to clearly communicate problems with others as an authority figure at the table and in their life. I don't necessarily think the punishment was unreasonable, but if it's not explained to them, it just comes across as arbitrary and vindictive.

Imo, the best way to handle issues like that is to set the rules and consequences, making them clear to everyone, and to be consistent in their application. Letting people off or being vindictive will just exacerbate things.

I think that was the right action, but you could have explained better. Instead of just "Ok, you stay at the tavern" something like "Ok, you can stay at the tavern if you really want to, but you do understand that will mean you're sitting here bored all afternoon while the rest of us play, right?"

Yeah you definitely showed that 12 yr old who is boss...