In the '90s, I read a book about a princess whose governess was a witch that mind-swapped her and a cat. The governess did this so she could control the princess. The cat who had the princess' mind ran to another kingdom and became the pet of the prince. The main story is the puppet princess coming to the prince's kingdom and the cat-princess trying to get back into her own body.
1 Answer
I think you might be talking about The Perfect Princess by Irene Radford, published in '95. It's the sequel to The Glass Dragon.
Just as you described, the princess Rossemikka's (can't vouch for the spelling) mind has been swapped with that of a cat to make her more docile and obedient- while the cat, guided by the princess' mind, becomes the closest companion of Prince Darville. He then has to figure out the whole conspiracy to save his kingdom and hers.
https://www.goodreads.com/en/book/show/803007
This is it on Goodreads, though it doesn't mention the whole cat thing.
Editing because I found this blurb:
"Hidden among dragons, cats, magicians, and a golden wolf lives the Perfect Princess for a new king. But who, and what is she?
Crown Prince of Coronnan, Darville de Draconis, fell ill after being kidnapped by a rogue magician and ensorcelled into the form of a golden wolf. Though he feels fully recovered, the Council of Provinces and his regent—the same rogue magician who kidnapped him—will not allow him to be crowned king until he marries the princess of their choice.
Princess Rossemikka of Rossemeyer comes with an impressive dowry and a vital military alliance. The problem is that she too has been the victim of a magical transformation and exchanged bodies and spirits with her pet cat. The placid and boring princess presented to Darville is less than suitable. However, on a magical night, with the aid of the deposed senior magician of the commune of magicians, the real Rossemikka is revealed to him. He will settle for no one less than his perfect princess, but time is running out. If Mikka is not returned to her own body soon, she will forever be only a beloved pet and not his queen. But how will his few friends and allies reverse the spell that traps her in an alien body, thus saving the love of his life and his kingdom from a power mad magician."