I am sure Zestu had the other eye for safe keeping. I think Obito brought Nagato's body to his lair to get the eye.
Black Zetsu was busy with his guerilla attacks before he got cut in half by that seven swords of the mist guy (forgot his Name), and white Zetsu was watching over Sasuke.
The Zetsu army joined the battlefield, in other words there was no Zetsu left to look after the Rinnegan.
Just in case there was one Zetsu left to look after the Rinnegan, it wouldn't make any sense mainly because A. Obito knew that the Zetsu army was weak, that's why he had them disguise as the Alliance so they would kill each other believing the person standing next to them was the enemy and to lessen their morale.
He wouldn't let a weakling look after such a mighty weapon.
And B. Obito is not a fool, he knew that even though Zetsu was loyal to him, they were still more loyal to Madara, so the best place to hide Nagato was the Kamui Dimension, no one else can get in and you don't have to fear any attacks from the inside.