This is Carpe Diem.
My god, is it easy to live! While I was doing a night shift at a PC room, I decided to play a daughter raising game out of pure boredom and nostalgia. But the ending she wound up with was... an Old merchant's concubine. When she got too annoyed and tried to find a different game to play next, a pop-up screen came up on her computer. [You are invited to our world! A place where you can get anything you want!] As soon as she clicked the yes button, she heard a butler's voice:"It's time to wake up, My Lady." Before she knew it, she had become the "daughter" of the game she just played! Ah, she probably would've chosen a better name if she'd known this. Rollypolly Perero. Why did a pack of cookies have to be in front of her when she typed in the name? Could a 24 year-old trapped in a 10 year-old's body successfully manage to become an adult?
The synopsis matches the question; the MC is working at an internet cafe and passes time playing a daughter raising sim, much like Princess Maker. She keeps getting endings she doesn't like, and goes to a different game, but as she enters the starting data, she finds herself in the game as the ten year old child she just created.
Her father is described as one of the top-four mages. After an incident, he gives her a set of magical earrings that changes her hair color from the initial silver to a dark blue, matching her father.