Potential quarrel with mother?

Honesty IS always the best policy. Just tell her the way you feel. She should understand. It is nice that you want to honor your Grandmother by remembering her however she would probably want you to go to the parade, especially if it was a parade she enjoyed while she was alive. Make sure this is the real reason you do not want to participate in the parade. If it isn't then you just need to be honest with your Mom and tell her why you do not want to do it. A Christmas parade is not an occasion that people should be forced to do something they do not want to.