family should be regarded as singular, because you are not talking about individual members of your family (who might all have differing ideas about when curfew should start), but the family as a single unit. This is how the word family is usually regarded in the phrase “my family”:
My family goes out for pizza on Sunday night.
But this changes when we refer to the family members indvidually:
My parents and my sister go out for pizza on Sunday night.
A similarly-labeled word would be class, which can refer to a classroom full of students:
The class does not like Ms Kolzik; they think she is a mean teacher.
Students do not like Ms Kolzik; they think she is a mean teacher.
In the first sentence, the word class is singular, so the verb acts as if the word is singular, even though a plural pronoun is used in the subsequent clause. However, I can also say:
The senior class votes in student elections next week.
In this case, class refers to the class as a single unit, so the verb is written as though the subject is singular. This can be tricky, though:
The senior class all vote in student elections next week.
By adding the word all, I’m now referring to the individual students as part of a group, so the verb switches over to a plural form
.each one of them will vote next week