J.S.
I don't think ANYONE handled themselves very well from start to finish in this whole comic tragedy, to be frank. This may be your husband's side of the family but these people ARE your family too. You're not an outsider. You married him, so you married his family too. You married all of the baggage and you continue to drag out all of the old high school drama along with them.
You could have chosen to handle the cousin differently. Returning rudeness with rudeness, which is how I'm interpreting "curt" to mean since the cousin responded unkindly, is never appropriate. If you always take the high road then they have no reason to scrape you up off the street as roadkill. You could have cut her short but killed her with kindness doing it.
In addition did you really have to tell your husband? Whether you handled it appropriately or not, you did handle it and you held your own against the cousin and anyone else. You clearly don't let anyone push you around and that's commendable. You had to have some strong idea how your husband would react to the news that his cousin was acting like a busybody since you described all of this behavior on his side of the family as "normal :-) "
My husband's family is pretty amazing and I love almost all of them. He has an aunt in particular that I actively dislike and has personally hurt me in the past. She has a reputation for being a shrew and she takes advantage of it. "That's just how she is, she's abrasive." Right. So I know the type. I've held my own against her and managed to put her in her place without ever demeaning myself or making myself come off poorly to anyone who might be observing us. I kept the incidents to myself since I'm not the one who came off poorly, but also because I'm an adult. And I don't ever want to make a habit of complaining about my husband's family. I may complain about my own, but I won't speak a negative word about his family even when he's ranting against them.
That all said, he's also an adult and what's done is done. You told him and maybe that's just how you guys do things. I'm sure he felt he was defending you. Can open, worms everywhere.
I wouldn't pretend nothing happened, as that never solves anything. Because this did originate with you and the cousin, then it needs to resolve with you and the cousin.
"Hi, Taighlyr. I'd like to talk to you, and I know that you're probably upset with me right now so you don't have to say a thing. I would appreciate it if you could just agree to listen. At MIL-Service, when you approached me with some questions, I felt caught off guard. They felt like personal questions that I wasn't ready to talk about and I reacted poorly. Then later at home, I told Husband about our interaction while I was still upset and you know how he can be... Me Man, You Woman... Me Big Protector... and now we have this situation that feels out of control. I'm sorry that things got this far out of control. I don't want this to come between us, and want to work on this. Do you have any ideas?"
If you use something like that, you're still not giving her anything personal and you're only taking responsibility for your reactions that propelled the current situation. You're explaining your reaction to her. Hopefully she'll hear the "I'm sorry" and assume you're apologizing to her specifically.
But if you two make amends then the rest of them have no excuse to continue acting like douchenozzles.