After some more Googling, I find that "мы вас похороним" and "мы вам покажем кузькину мать" were allegedly spoken by Khrushchev on different occasions.

But I'm still not sure who "Kuzka's mother" is! Or, more to the point, who is "Kuzka"?

I would guess that Kuzka was an evil monster whose mother was even worse, and so показать кому-нибудь кузькину мать is like saying "If you don't stop misbehaving, I'll call Voldemort's mom!"

(Or substitute "Hannibal Lecter's mom" or "Dracula's mom" or "Grendel's mom," if you like.)

But that's only a guess...