AYC gave great reasoning. I agree with him/her…
I’m trying to think if one of my parents would apologize to me what I would think of it-
It definitely would make me respect them more for admitting if they did something wrong and it would teach me a great lesson that adults too make mistakes and ask for mechila even if it is to someone younger than them or of less stature- so I def think it is a good idea to ask them.. not so sure halachically if it’ll really count or if you need to, but it shows great parenting IMHO. But obviously don’t go overboard.. Maybe one or two things or in general something..