I don't think you should look at it in a perspective of "who is right", but rather "who is hurt" in this situation.
Sure, you could be just talking out of your ass when it comes to threatening to beat up that drug dealer. But put it in their perspective a bit. You got mad at this drug dealer, so mad that hypothetically, you were willing to risk yourself and your family to go beat up this guy for your cousin.
Now, you said you don't talk to your cousin much at all. So, you've projected that you're willing to go to drastic measures for the sake of someone you know less than your BS.
So, who is hurt if you followed through with this plan? Well, the drug dealer for one. But also your BS. Quite frankly, no matter how justified it is to beat that guy up, he isn't worth risking your family over. What would happen if your cousin found themselves in a similar situation again?
But, if you don't do it, then no one is hurt. You're not risking everything for some ill-conceived vengeance. If your cousin is in that much trouble, the authorities should be involved and nothing more. Don't waste your time.
I guess how I'm interpreting it, from what little there is, you threatening to beat them up was pure bluff. But, even so, the fact that you'd say something like that for the sake of your cousin and not your BS speaks words to them. Have there been any great sacrifices you have made for your BS like that?
It's odd, but I think after the A, BSes will compare themselves to everyone you know, even relatives. "If he's willing to do that for him, what's wrong with me to the point where he wouldn't do the same?"