I'm an administrator for an estate. A large part of my role is checking up on the paperwork and standards of the work of other colleagues. The concierge team are supposed to hand in paperwork to the office on a daily and weekly basis but they are really bad at it. My manager asks me to ask them to hand it in and complete it if incorrect. I feel uncomfortable about that anyway because I'm not a supervisor or manager, then my colleagues ignore my requests and now I'm working from home due to COVID lockdown they're ignoring all my emails requesting paperwork or calendar invitations for essential jobs. I feel really stuck here because I don't think I should be in this responsible position, my manager is annoyed that my emails are not getting responses but I'm a colleague not their superior. It's a bit confusing.
I would suggest bringing your boss the problem (lack of follow through by co-workers) and a solution. As a solution I'd suggest a weekly report of your tracking of this paperwork along with notes on reminders sent out, emailed to your boss a specific day each week with anyone who has an outstanding request CCed. Bringing your boss on board that a problem exists and giving them a solution to the problem makes it much easier to get buy in. This report helps make it perfectly clear that you are on top of this responsibility but there are specific instances (with dates and times) of lack of follow through from others.
Don't stress yourself over something that is your boss's problem. She's got tools like the company bonus/discipline procedures that she hasn't given you the authority to use, and managing these people is her job, not yours.
You can try to help her by providing all the information she needs, and making sure no one can claim they didn't know they were supposed to do something, but that's all you can do.
If this causes you any difficulty in doing your job, you need to discuss this with your boss too.