I think that family tendency means that it is something you tend to do as a family
What you tend to do as a family together
It means there is a tendency in the family for something to happen,( ie a disease,) Many tendencies are genetic but ,then because we are a product of our genes and also of our environment then the way/s that someone is raised also can produce a family tendency for things to happen.
Something inherited or copied from a particular family by someone who is a member of it.
Something to happen like a disease that travels through the family