The Unicorn Trilogy is a series of books by Tanith Lee:
Black Unicorn: The Muggle daughter of a sorceress, Tanaquil, accidentally resurrects the titular black unicorn, who whisks her away to Sea City, where she discovers her father and half-sister Lizra, learns of her own unique magical capabilities, and helps the unicorn return to the perfect world.
Gold Unicorn: Tanaquil is reunited with Lizra, now a conquering Empress, and is coerced into making a war machine in the shape of a golden unicorn work, causing a gateway to a hell-like world to open.
Red Unicorn: Once reunited with her mother, Tanaquil must face her own inner demons in the form of an Alternate Universe, an Evil Counterpart, Tanakil, and the red unicorn that binds them.
Abusive Parents: When Jaive believed that Tanaquil was talentless, she more or less neglected her. Even after they reunited under better terms, she was so caught up with experimenting with Worabex that she accidentally caused Tanaquil to enter her Inner World.
On Lizra's front, Zorander only bothered with her when she could make him look good. Also, he tried to have Tanaquil arrested and executed (though he likely didn't know she was his daughter).
Anguished Declaration of Love:Subverted, after Honj finds out Tanaquil is near death, he makes this to Lizra, declaring that he loved Tanaquil all along. As it turns out, Lizra wanted an excuse to break off her engagement to Honj anyway.
Arranged Marriage: Lizra claimed that she was already betrothed to someone to turn down The Emperor's proposal without telling him she couldn't stand him.
Later, she agrees to break off her engagement to Honj so she could enter one with an overseas king and consolidate their power.
Barrier Warrior: One of the gifts the black unicorn gave Tanaquil and the peeve in gratitude is involuntary personal forcefields that protect them from anything from a wasp sting to falling out of the sky.
Chariot Race: Of an interesting variant: the chariots are rotting chairs.
Everything's Better with Princesses: Lizra in the first book. She also tends to lie and say the people she befriends (such as Tanaquil and Honj) are royalty as well to make them look better in others' eyes.
Humans Are Bastards: Which is why their world is imperfect. Just stepping in the perfect world causes ruin to it.
The hell-like world exists because its gate is a war machine created by Lizra and her army.
Inadequate Inheritor: Part of the reason Tanakil is so resentful of her half sister Liliam is that despite being older, she was passed in the line of succession because her mother ran away, while Liliam's stayed.
Muggle Born of Mages: Tanaquil was initially thought of as this because she didn't seem have to have inherited any of her mother's magical capabilities, and was more like her father in her mending skillls. Her magical ability is in her mending skills
Standard Hero Reward: Everyone presumes that this is Honj's reward for 'saving' Lizra from what the people believed were kidnappers. It ends up being broken off so Lizra could marry an overseas king and Honj could be with Tanaquil.
Stealth Pun: There is a type of animal called a "peeve", and Tanaquil has one as a companion. You might say she has a pet peeve.
Talking Animal: One of the peeves around Jaive's fortress becomes this due to the excess of magic, and becomes Tanaquil's familiar.
Well-Intentioned Extremist: Lizra, after becoming the Empress Veriam, whose intention in conquering all those lands is to create a perfect world in their world.
What Kind of Lame Power Is Heart, Anyway?: Tanaquil's magical capabilities lie in her ability to mend and fix anything, sight unseen up to and including a broken heart, and render it incapable of ever breaking again.