Sybil Russell in the Chalet School series, partly due to her resentment at having to compete for her mum Madge's attention with several older cousins. One nasty incident involving a kettle and her little sister Josette, later, however, she gets over it.
Scabmona from Robin Jarvis' Deptford Mouselets book Fleabee's Fortune. She revels in being as vile and unpleasant as possible. As they are rats, her parents are actually proud of her rude behaviour, while they are ashamed of her polite older sister Fleabee.
Willa Jean. She ages from book to book, but Ramona still can't stand her. Willa is such a spoiled brat who doesn't get in trouble for anything she does because, don'tcha know, she's just sooo cute (though she does try patience on some occasions), that you just gotta hate her.
Ramona herself was like this when she was younger. A running gag was that when her older sister Beatrice and her friend Henry would play checkers and ignore Ramona, she'd forcibly break up the game by ramming the table with her tricycle. Ramona was actually mortified when she was told she'd been as bad as Willa Jean once.
Penelope from The Serpent's Egg trilogy does this, except everyone believes her insane stories. Except, of course, the true one about that magical elf land she goes to with a Druid. She also happens to have a toy poodle which she always paints a new color each book... And yes, she does eventually wise up.