The Lord Of The Rings appears to be the "One Ring" not Sauron! Sauron himself can't control any ring without one ring. Sauron appears to have no power over the elven rings! If anyone who has enough power to use the One Ring he can control all the other rings and become the lord of the rings. There are many many examples that proves this. I am not sure why people think Sauron is the Lord of the Rings. It appears to me it's the ring of power itself and not Sauron that is the Lord of the Rings. So is it Sauron or the Ring itself that is Lord of the Rings?
Yes the One Ring or the Ring of Power controls the other rings.
Three Rings for the Elven-kings under the sky, Seven for the Dwarf-lords in their halls of stone, Nine for Mortal Men doomed to die, One for the Dark Lord on his dark throne In the Land of Mordor where the Shadows lie. One Ring to rule them all, One Ring to find them, One Ring to bring them all and in the darkness bind them In the Land of Mordor where the Shadows lie."
—J.R.R. Tolkien's epigraph to The Lord of The Rings
However your mention of the three elvish rings is incorrect.
The greatest three Rings Celebrimbor crafted alone. So Sauron took no part in their crafting. He had no opportunity to corrupt them and turn them evil.
The Three that remained to the Elves were carefully hidden from Sauron. They were not created as weapons of war or as a means to dominate others; their purpose was to preserve the beautiful Elven domains where their wielders resided, and to aid in healing and resisting evil. However, they were still linked to the One Ring, and whoever wore it could, with effort, see the thoughts of those who wore the Three.
So at most Sauron might have been able to read the thoughts of the elves (and Gandalf) wearing the three rings, but nothing more.
But he could not have turned them into wraiths, or controlled them.