Webtoon/manga about a female character who practices black magic in her first life and is accused and killed by the child she brought up

Question

The female character practices black magic in her first life and is accused and killed by the child she brought up with her. She is then reincarnated into a baby's body.

This baby has one dark-haired uncle and one grandfather. And at first his uncle wants to kill him but then he starts to like him. The female character always plans to escape. He goes to the orphanage on his first escape. Then she returns to the mansion, stays there until she is 18, then runs away again.

This was adapted from a manhwa novel. The female character is always walking around with a pacifier in her mouth. The father of the female character has passed away. His uncle is divorced from his wife. She also has one male cousin.

Answer 1

This is Gimme That Pacifier!.

From Baka-Updates:

Betrayed and executed by her pupil, magician Hela Sylopia is reborn as the neglected infant granddaughter of a rivaling nation's duke. To make matters worse, her family doesn't remember her name, and the maids don't care what happens to her! But when she discovers that having her pacifier in her mouth can expand her mind, Hela uses that to her advantage to survive, get rid of those who stand in her way, and start plotting her revenge. Will Hela succeed, or will she wish she'd never been reborn?

Hela Sylopia, a great mage, is accused of practicing black magic by the High Priest, Melane -- once her trusted pupil, whom she helped elevate to his current position -- and subsequently executed. Just before her death, she swears vengeance upon Melane.

She then wakes up in the same world, not long afterward, as Sherina, an illegitimate baby girl in a noble household. Her father, a noble, is recently deceased and her mother, a commoner, isn't in the picture, so she's raised by maids and given a pacifier to keep her quiet.

Her paternal grandfather, uncle and young, male cousin live in the same mansion and don't care much for her initially, especially the uncle, who has thoughts of killing her. Over time though, her new relatives warm up to her and more fully acknowledge her as part of the family.

She knew her current grandfather and uncle in her previous life, so she recognises who they are right away. She still intends to avenge herself against Melane, but her magic is much weaker in her infant body, so she has to bide her time until she gets older and more powerful.

Shortly after she turns three, her grandfather and uncle decide it's time for her to be sent away to an academy traditionally attended by members of their family. However, she views this as a rejection, and decides to run away to an orphanage, using a teleportation spell.

This occurs in chapter 40, the second-to-last chapter of the manhwa currently translated to English. I'm guessing that some of the later events you mentioned are from parts of the novel which have yet to be adapted to the manhwa, which is still ongoing.