If Emperor's Divide is hidden, can I move a unit from another battlefield?

No — if you play Emperor's Divide from Hidden, the units you move must all be at the battlefield where you hid it.

Rule 811.1.d.2 restricts a hidden spell's choices to options at the battlefield it was played from, and this card's own example uses exactly this scenario: all units chosen for the spell must be at the same battlefield it was played from. So a unit sitting at a different battlefield can't be selected. If you play Emperor's Divide normally from hand (for its cost, at Action timing) you're free to pick any battlefield — the restriction only applies to the facedown play.