There was no rebellion in Austria during his reign, but the story might be based on https://en.wikipedia.org/wiki/Milan_uprising_(1311) where Leopold did play a big role.

https://www.habsburger.net/en/chapter/duke-leopold-i-sword-habsburgs
https://en.wikipedia.org/wiki/Frederick_the_Fair
https://en.wikipedia.org/wiki/Louis_IV,_Holy_Roman_Emperor
He did also attempt to get his brother elected as King of Romans and quarreled with the Duke of Bavaria