You can appeal the discipline up through your management chain and/or to the HR Director. Your company should have written guidance in the form of a policy describing how it deals with employee complaints, including appeals. (I'd want to know what specific company policy I allegedly violated.)
Unfortunately, it sounds like the nepotism in your Company may end up getting the best of you. You've seen one reason why nepotism gets a bad rap. Strongly consider whether this is the type of organization whose values and employment practices align with your personal goals. The daughter has been empowered, I fear, by what has happened to you.