The choice of "Bidens familly" by the right-wing is just a way to smear Joe Biden indirectly, as they have nothing on him.
It's very simple, they say "the Biden crime familly", because they cannot talk aboutJoe Biden's crimes.
The left-wing (or so-called) doesn't need to say "the Trump crime familly", as they can talk directly about Trumps crimes, convicted felon, etc...