What kind of document do I need to write to have my mom relinquish her POA to me?

My Dad had my Mom as his primary Power of Attorney and if she was able to be POA, then next in line was my name. Thus, it was automatic.

For me, I wanted my Mom to still have the authority to be Dad's POA as per his original request. And it was up to her whether she felt she was able to make a decision for him or not, my Mom was in her 90's, legally blind and could barely hear.... so any time my Dad went to the ER, I went with him as his POA, as my Mom didn't want to go as it would be too confusing for her due to her eyesight and hearing. It worked out well.

Your mom would need to write the document resigning not you.
But as GA said, it should be spelled out in the POA.

You need to carefully check the wording of the POA. If you're an "alternate", there likely is already wording in it that allows you to act.