Well she's 72 years old, she might want to get used to the fact that now a days she never going to have a supervisor that's older than her. Maybe she should quit if she doesn't like to listen simple as that. I'm sure other people would enjoy to have her job and that will listen.

That is very likely but not your fault at all. The person my sister did have a problem with was about 10 years older than her and IMO that's not an excuse to be rude to your supervisor.

This lady is probably using the age difference as an excuse, and she probably feels like she should have it, or not have to struggle to make a living at her age. Than here you come, and get a promotion and more money, and it might not seem fair to her.
The harsh truth for her is that she put herself in this situation..why didn't she work to get promoted or move up in the company? She needs to stop the attitude, and get into line or quit.
Just make sure you log each time you have an unpleasant run in with her and keep it filed somewhere safe, because it takes a mountain of paperwork to write up and fire people these days.