You are not really changing your status from US to Canadian citizen. You are already both.
I do not know if it will affect your parents taxes if you go to Canada to study. I suppose they should ask their tax advisor about that.
What you are doing really only has to do with your university and their registration office. If they say that you must initially apply as an international student you just have to send them a copy of your citizenship card to prove that you are a Canadian citizen and that should get you the lower fees. You should also get a Canadian passport, see
http://www.pptc.gc.ca/form/index.aspx?lang=eng but remember that as a US citizen, you must always use your US passport when you enter the US. When you enter Canada, you can use the Canadian one.