Fun fact: When you are a Serb reading this sentence naively, trying to translate word for word, you get "Oni su u mojoj mami", which means "They are inside my mother".
I don't think there are. Sure, you can say "Mamy mamy" (We have moms) and the same thing can mean "Mom's moms", but I just thought about it right now (probably not the first person in history to think of that though), I don't recall hearing any jokes about that.
I continually object to the use of mom and dad here. They're too colloquial. I'm more likely to say "my mother's house" to the average person outside my family.
You can use "mother" if you like (at least when you use the option to type your answer), but "mom/dad" really are the most straightforward equivalents of "mama/tata".
I like to think of it as being "at mom('s place)." Kind of like the English equivalent:
-I'm at Anna's place - Jestem u Anny.
-You're at the doctor's (clinic) - Jesteś u lekarza.
-He is at the barber's (shop) - On jest u fryzjera.