Muldrotha, the Gravetide is in play under my control. Is this legal?

1. Play Vault of Whispers from my graveyard, playing it as a 0-casting cost artifact.
2. Play a regular land from my graveyard, as a land for the turn.

Or am I still breaking the "1 land per turn" rule?

vault of whispers isn't a 0 cost artifact

if you can play 2 lands you could play vault of whispers as an artifact and a different land as a land, but otherwise you would still be breaking the 1 land per turn rules.