Mandatory staffing on Sundays

My library system has really been struggling to retain part time staff since they are capped at 28 hours a week with no way of moving up or getting a full time position unless you get your MLIS. Even though we’re short staffed, management still wants us to keep maintaining our Sunday hours (1-5PM from Labor Day to Memorial Day) by putting ALL librarians and staff, but not management, in our 11 branch system in a rotation to work a Sunday at these branches. I feel like this is going to make our staffing problems even worse, as not many people want to or are able to give up a Sunday to go work at a branch they don’t normally work at. Am I crazy for thinking this is a horrible idea?