She had brown hair like her mother
And he did punish the mother
She was locked up in the inner palace
They worded it like she just wouldn't be allowed to go to fancy events and stuff, but no. It basically means she's been imprisoned in her room for the rest of her life. She won't be able to meet her family (including her husband and daughter)
or friends and she will likely only have a servant that will bring her food.
It's how they used to punish royals and nobility when they didn't want the scandal of having them executed or exiled. It's definitely better than a regular prison, but not by much. They might even subtly kill her off in a few years with a fake illness.
If he'd had her executed immediately, the daughter would have likely not had a good life. There is still a chance it's his daughter, she's most likely not, but it was never proven that she wasn't and I doubt the king would want to risk it.
The lil girl had orange hair???? So its obvious its not the emperors daughter wth! And he still kept it and killed the man and left the women without punishment like what the fuck