Does being a durable POA mean one has to be an emergency contact or can I continue to be as I have been for 12 years?

Contact for what?

Does someone have Medical POA? That is the person with authority over your mom's person. The durable POA has authority about finances and legal matters.

Is your mother at a point where she cannot make this decision herself? If she is still competent to understand the issue she should be the one deciding who she wants as emergency contact.