Odd. "I have a family in a village" sort of sounds like someone is leading a double life, with two families. I put "I have family in the village.", i.e. maybe my brothers or my aunt live in the village. (It was accepted.) Which is the more likely interpretation?
Even in Ukrainian this sentence sounds strange to me. I also feel that it's about a double life, but I seriously doubt that that's what course creators had in mind. Anyway if you want to say that all of your close relatives live in village say Моя сім’я живе у селі (My family lives in a village) or if you have some relatives in a village say У мене є родичі у селі ("I have relatives in a village", not "family" )
I've been playing this game with myself where I imagine all sorts of strange stories from these seemingly innocent sentences. It's quite fun.
Here in the US, "family" is used to describe immediate family (Husband/wife/kids) and extended family (grandparents/aunts/uncles/cousins). We use the term "family" and "relatives" interchangeably.