I’ve had a lot of luck with using Robo Rally to get people into boardgames - dead simple, but chaotic and good for making people not feel stupid when they fuck up (because the results are usually hilarious). Eight Minute Empire is nice and straightforward. Pandemic can work, too, but you need the right group.
If you’re including card games, Fluxx is good for newcomers. So’s Love Letter.
A lot of it comes down to what sort of style you think would sit your family! Do they like silliness, or do you think it would get on their nerves? Co-op or cut-throat competition?