There isn't actually any suitable idiomatic word/phrase that's pretty common and casual and can be used in day-to-day conversations and writings. None of the other answers address this. Your context gives the impression that it's a normal piece of writing. Second-degree relatives, extended family, whatever you say— they're technical terms and don't even specify that it's your aunt, uncle, and cousins and not your grandparents. Most people will not get you easily and it'll probably make you sound awkward or nerdy.
The word you want is just too too specific. Just say it—my aunt, uncle, and cousins. What's wrong with that? It doesn't do to be lazy and sloppy in writing.
In fact, people will like hearing more about them. Describe them better if you can. It'll give you a topic to talk on, triggering conversations. Short, concise, to-the-point writing is for academia.
X: You know, my aunt, uncle, and my cousins came to see me yesterday. I toured around the city with them.
Y: Oh, cool! It must have been exciting. Did you have fun?
X: Yes, my cousins are such cuties. Amanda's 5 and she...
On a second note,
you might consider — my aunt and her family or my aunt's family. Personally, I like the former better:
Today I toured around the city with my aunt and her family who came to visit me.
An aunt sounds odd to me. You don't need to hint that you have more aunts and it's just one of them. It's your aunt and not somebody else's — that's more important to focus on.
Alternately, if your uncle's the direct relative and your aunt his wife, then say "my uncle's family" instead.