Hello Sean and welcome to Seven Forums.
If you paid for the computer with your own money, and if you're paying for your own internet connection, then I don't think your parents should have any say in what anti-virus suite you want to install. But if your computer is part of a home network paid for by your parents, then they might have a legitimate concern about malware. So perhaps a better solution is to provide your parents with some recent anti-virus test results and show them that Norton isn't the only AV company in town; that there are other free and paid companies like Avast, Avira, BitDefender, Comodo, Kaspersky, MSE, ESET, Vipre, etc that may be better than Norton. As far as making "major changes" I would again have to ask who paid for the machine.