SOLVED. Children’s book: Man with flaw has to learn from woman how to care for others in wilderness

[Amanda]

The book I’m looking for is a fairytale I read when I was a child; it must have been some time between 1997 to 2002ish? There was a man with a flaw (either spoiled or conceited/vain, may have been a prince) and there was a woman who lives in the wilderness or mountains in her own cottage. I remember she had to make her own bread, had a sheep, and maybe had a limited amount of seeds, so she had to use her resources wisely. There was also an old woman and the prince had to carry her on his back. The woman taught the man how to care for others and once he learned the errors of his ways the two fell in love.

Edit/update: the book is The King’s Equal by Katherine Paterson