I am secondary power of attorney for my Mom. She does not have a durable power of attorney for health care. She is in a nursing home. I handle all of her finances and her health issues. Lots of time, my sister has to come in an sign paperwork. This is burdensome.
If, on the other hand, it is you who is finding it a pain in the neck to have to contact your sister every time something wants doing, you can bolster your patience by reminding yourself that it isn't your job to get these things done promptly so they will just have to sit on the 'to do' list.
And if the NH is grumbling, they can grumble at your sister. Not your fault, not your problem.
I don't know how a primary POA legally and officially resigns. That would be a very good question to ask the lawyer who drew up the POA. If that lawyer is no longer available, then find a lawyer to ask.
You don't have to file for guardianship to become primary POA as the secondary POA if she wants to resign form being the primary POA.
Perhaps you are looking at an attachment to the Will that designates a POA for health care?