OP said the child didn't get much sleep because of problems with her younger sibling.
It is quite possible the child is having some jealousy issues or other issues causing her to act out. Not to mention not having a good night sleep. I know my concentration is a little off if I haven't slept well. Probably a little harder for a 5-year-old.
I don't think it is prudent to jump to punish a child when it is out of character for that child to misbehave, especially if the child had already received punishment.
Yes, it will humble her. It could also demean her. I'm definitely no expert, except by experience. When this child has future emotional issues that she is not quite sure how to deal with, she defintely will be too humble to act out or to try to talk to her mom about them, because she has been taught not to. She'll just keep them locked inside or act out in a way she won't get caught.
A 5-year-old is not to young to be asked why she acted the way she did, or to discuss it. Why do parents have a knee-jerk response to just impose some kind of punishment without trying to understand first?
I'm not saying an apology is wrong, I just don't think it should be yet another punishment. If anything, mom should discuss it with her, like... "honey, I really think you owe your teacher an apology. What do you think?" Let it be the child's decision. It's good training to let a child make decisions like this.
The teacher punished the child. That's her job. It is our job as parents to try to understand our kids and open lines of communication and let them get used to making decisions.