First, "the family" refers not only to her family but also to anybody else's family so it's a general concept (to which everyone can relate). Second, even when "the family " refers to a specific family, it's still usually ok to say "in the family" but other pronouns are also possible. It was like having a death in the family.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.