I think demanding an apology is correct whether the person wants to or not. Your parent should be the first one in line to apologize and set an example of doing the right thing. If they are reluctant, I would demand it.

People in general need to be held accountable for their actions. Perhaps no one ever demanded an apology from your mother before? Maybe it's time for her to learn something now? You deserve to be respected just as much as she does. Sometimes we have to take a stand. This may be the time for you.