1. My family used to live in London, didn't they?

2. My family used to live in London, didn't he?

3. My family used to live in London, didn't she?

4. My family used to live in London, didn't it?
---------------------------------
Which tag question is correct?

Only #1's tag question is correct. The word "family" is a collective noun and in reality includes more than one person.

My brother used to live in London, didn't he?

My aunt used to live in London, didn't she?

My dog used to live in London, didn't it?