The Hollow Kingdom by Clare B. Dunkle is one of my favorites for personal reasons, and not just because the protagonist is also named Kate (a fairly popular name for Girls Underground, though, as I can think of several other examples).
Kate is a teenager in Victorian England, who has come (with her younger sister Emily) to live with their aunts on ancestral land after the death of their father. One night the sisters get lost in the woods and stumble upon some strangers who fill Kate with dread. She discovers that they are goblins, and is terrified that she and her sister will be captured and taken away to their underground kingdom (another story where the otherworld is literally underground).
The king of the goblins desires her as his bride. But she has another adversary as well, her human “guardian” who does not have her best interests at heart. He hopes to send her away to an asylum after she rants and raves about goblins.
Eventually, her sister is abducted and she must sacrifice herself to the goblin king to save her (unlike Jareth in Labyrinth, this goblin king is a goblin himself, not diminutive but definitely grotesque in certain ways). She is helped occasionally by a strange otherworldly cat with magical powers. The door between the goblin world and above-ground can talk – a common occurrence in these stories.
The twist here (welcomed by those of us who can never understand why the girls always run from their intriguing adversaries and go back to their boring lives above) is that after her terror abates at being married to the goblin king, she comes to love him, and when he and his kingdom are threatened by a terrible power, Kate comes to their rescue.