Fantasy novel where two characters (male & female) get sucked through a portal. He a prince, she a trainee wizard

Question

I'm searching for a fantasy book published before 1993 that deals with 2 characters in a kingdom that get pulled through a portal in the wall to other lands. They have to learn how to work together, and yes, they fall in love.

Characters:
Young, clumsy female just beginning to learn magic Young prince too busy to remember her name. Shape changing mist that always has green eyes.

Random things: They end up battling each other with magic. He gives her a mirror and puts a spell on her hair so it can't be rebraided.

Any help you have would be much appreciated!

Answer 1

This sounds like The Hidden Realms by Sharon Green.

Prince Bariden and the sorceress Chalaine are tasked with solving a magical crime. They start out not getting along due to actions from each of them. When Chalaine first meets Bariden she is carrying a magical ball of water and accidentally drenches him. The story points out that many people around her suffer similar misfortune frequently due to her being clumsy. Bariden offends Chalaine by forgetting her name and rushing off without waiting for her.

They fall into a trap that sucks them into a series of worlds that are connected by portals. They have to work together to get to the next portal as they move from world to world.

At one point they do battle each other in a contest.