As soon I heard the word "domingueando", and found out what it meant, I was in love with it. Not that it's all that special, I just get a kick out of it.
"domingueando" comes from the verb dominguear. And you may have noticed the simularity to the word "domingo" in there. "domingo", meaning Sunday, of course.
So what does it mean to "dominguear"? It means to put on your "Sunday best" as we might say in English. In other words, you're wearing your church clothes. You know, your nice slacks and a fancy shirt, and perhaps a nice dress for the ladies.
So with that bit of basic information we can translate our sentence:
Toda la familía anda domingueando
The whole family is all dressed up
Here's another example:
Hoy me voy a poner mis pantalones de dominguear
I'm going to put on my Sunday pants
And FYI, it doesn't have to be Sunday for you to "dominguear".
It's never a bad thing to "dominguear" de vez en cuando (once in a while), and now you can even talk about it in Spanish!