ZZZ The King's Daughter

Dad: BAMF, kuudere, beastly Duke (not the king, but more powerful than the king, so?)
Daughter: An abused (by her mother), illegitimate sweetheart AKA "The pink cub amongst panthers"
Type: Reincarnation isekai
Note: This one sports an AWESOME daddy (from the start) and an AWESOME brother.
*HIGHLY RECOMMEND*

Dad--ahem, I mean--Mom--ahem, I mean--Family: Scary, BAMF Duchess, her bear of a pushover husband, and her BAMF sons (all ready to fawn and dote on our little girl)
Daughter: Abused, born-as-a-sacrifice cinnamon roll
Type: Fantasy
Notes: Not royalty, but Mom can push the king into doing most of what she wants. (Talk about influence!) Again, not really isekai, in the essence that no one transmigrates or anything, but the world feels like an isekai, and it's adorable.
*HIGHLY RECOMMEND*

Father: the insensitive king determined to not fall in love
Mother: reincarnated as Snow White's mother
Daughter: the cutest little ball of fluff ever (by the novel)
Type: Transmigrated into a Queen's body
Notes: The main character is the Mother, but it's all about the king's daughter, so...

Dad: Kuudere, overprotective archmage (not the king, but hey, a powerful bitch is still powerful)
Daughter: Abused (by foster family) cupcake, a little weak-spirited.
Type: Fantasy

Dad: Conflicted but loving demon lord (not king, but kind of a king? still too early to tell)
Daughter: Abused (in her former life) dumpling
Type: Reincarnation isekai

Dad: BAMF tyrant Emperor softened by fatherly love
Daughter: Spoiled only child
Type: Reincarnation isekai

Dad: BAMF misogynist King unknowingly doting on his daughter
Daughter: Calculating daddy's girl
Type: Reincarnation isekai

The Duke's Daughter, but had a similar vibe.

Daddy: King
Daughter: Former Archmage

If this trend keeps up, I'll need a new list.
She's reincarnated not as the daughter, but as the villain's mother!
Mother: Reincarnated orphan with a love for children and more than enough maternal instinct to spare.
Son: Cute but yandere son of a duke, with a budding mother complex.
And, for kicks, throwing in the father makes a good family salad: the overbearing duke.