I was not sure about this game but it worked out well when we played it, one of a series of games with improvisation and category themes, where each player takes a turn. Word Association, If so and so was an animal, and even Mornington Crescent are related games. All quite short and can be included in the series.
Basically, in my family impressions, each player in turn thinks of somebody in their family, and answers questions ‘in the style of’ that person.
The trick is to choose individuals with particularly idiosyncratic characteristics, but then exaggerate them. The aim is to be kind, to laugh with the person, not at them. It is better if everyone asks a question, just one in turn, to the player who is doing the impression, then everybody guesses immediately who the target impression is of, so keep the rounds pretty short.
We always play this game infrequently, as it can be tiresome unless only used once a year or so. A good tactic is to choose a person with a certain accent or mannerisms, or possibly someone in the room which allows you to copy the body language. But be careful the impression is never offensive-only affectionate.
It is not necessary to have any scoring system with this game. The fun is from answering the questions, these are best kept fairly generic ‘what did you do today?’ ‘how are you getting on?’ or very specific such as ‘what is your favorite hobby?’
You need a pool of about 20 people to choose from, so grandparents, aunt uncles and cousins can definitely be included. Also any pets. It may be some of these are obvious, but no guessing until the round is completed then everyone guesses in turn.