Can anyone explain the grammar of
einer Ihrer Familien to me ?
Gibt es in einer Ihrer Familien auch eine interessante Person wie Onkel Willi?
familien is plural
"Einer" is dative because "in" takes the dative where there is no motion or change of state. Implied is "in einer Familie".
"Ihrer Familien" is genitive. The meaning is "of your families".
(Don't forget that "Familie" is a noun so it has to be capitalized).
We end up with
Is there an interesting person like Uncle Willi in one of your families?
This sentence translates to "Are there any interesting persons like uncle Will in one of your families?"
There is not much more to it. "eine Ihrer Familien" (Genitiv) refers to any one family of the audience's families. "in" needs either Dativ or Akkusativ depending on whether it is a direction/change of state (Akkusativ) or a constant position/state (Dativ). Since the interesting persons are already parts of the families we need Dativ and thus "eine" becomes "einer". This is the feminine singular Dativ form. If we'd been talking about how Will became part of the family, we could say "Es war ein großes Glück, dass eine interessante Person wie Onkel Will in eine eurer Familien aufgenommen wurde". This is the same structure but since there is some kind of direction we use Akkusative thus "eine eurer Familien".