What time [does x do] your family cook their dinner?

I agreed with that, but it has to be a distinction as whether the family members are acting in unison (simultaneously) or if we are thinking of them as "going solo" (individually/action restricted to every one of them).

My family does not give me permission to be outside after 10pm. (example from ell.stackexchange.com), "does" is used because we think of it as "everyone of the family" acting in unison. It´s would be a "concerted action/somehow agreed upon action" whether all member live under the same roof or not.

In the example "The class does not like Ms Kolzik; they think she is a mean teacher." It´s about the feeling that is thought as "in unison" So, one use DOES here.

To make a disctinction, that is, to say that not "everyone" of the class like Ms. Kolzik, the native would problably use "Students do not like Ms Kolzik; they think she is a mean teacher."
This mean that in the second sentence, if a single student don´t think she is mean then the author can´t say that "the class" is unanimous in that feeling.

With that, I take it back that "their" has to be about a group in this case. It goes with the thought whether you think about your family in terms of unanimity (or acting as a whole) or individualy.

Anyway, I should say that most of the time, family-as-unity-wise people use DOES. And to avoid ambiguity they would say "family members" for instance, to talk about individual action (then DO would go along with it.)

https://ell.stackexchange.com/questions ... do-or-does

It´s really an interesting and sometimes tricky issue, he hee.