I guess I'll throw in my opinion on this matter. Nothing else to do at work anyhow.
This is a sensitive subject. On one hand, threatening can be harsh sometimes and, honestly, may have not been the best course of action in this situation. Usually with kids like the one you described, I have come to find that the best course of action is to let it go. Yeah, the kid gets away with being an arrogant, pompous little jerk, but you just have to feel sorry for that kid later in life cause that kind of attitude leads nowhere.
On the other hand, there are a lot of good factors in this story.
1. You offered to pay a kid, who was playing in a creek, money to retrieve a disc
Most would have just walked up and said "Hey, could you toss me that disc?" You offering money right off the bat is very notable and beyond what most would have done.
2. When you knew the kid found 2 discs, you were going to offer more
Some people would have just still only payed the $2 and tried to get away with it. Again, very notable and beyond what some would have done
3. You tried to reason with the kid and even offered MORE before getting verbal
This shows that you had enough patience to try and talk him down. Maybe the kid was having a bad day, maybe he just needed to get a little something more that you were more than willing to give, and gave; I think this was another good move.
4. You let the kid mouth off a lot longer than most and, as you said in a previous post, you weren't really going to get physical
I was really relieved when I saw that you said that things wouldn't have gotten physical. There are some messed up people out there who may have; I'm glad to see you're not one of them. Also, most people would have shot off long before you did. Patience is a virtue. And finally, the threat was the last resort. This kid had plenty of opportunity to do the right thing and CHOSE to be an immature 3 year old going through the "mine" stage.
All in all, threatening is a moral standpoint. Personally, I may have just "let it go," but in saying that, I also believe that the situation was handled the best that it could been other than just saying "You know, you're not worth it." The kid has got a lot of things to work out in life and probably needs a hard lesson or 2 to get back on the right track (and will in the right timing). We can only hope that later in life, he realizes that you tried to do the right thing first and that he was the one being a jerk.
Also, with you posting this story and asking "Did I do a bad thing?," maybe you are feeling conflicted about it as well. If that's the case, just take it as is, can't do anything to change it now, you weren't completely in the wrong, and you did handle the situation in a very mature manner. But in most opinions, threatening either needs to be the last resort or not even in the equation.
And I'm with you. When I write, I write novels