Ultimately, it is your mother's decision as to whom she grants certain powers. So, you and your sister can argue until the cows come home; but it might not make any difference.
Typically when someone drafts a power of attorney, they expressly revoke any and all powers of attorney that predate it. What your sister is requesting is clumsy and awkward. Ask her how she would feel if your mother divided the granted powers between the two of you instead of overlapping them. One could control certain functions and accounts while the other controls other functions and other accounts. Each could be the successor attorney in fact (person to whom the power was granted) for the other in case either of you becomes unwilling or unable to perform his/her duties. Your mother might agree to that to keep you two from bickering.
These are just my thoughts. I am not offering specific legal advice here. Plus, you and your sister are not the ones to advise.
Some of this may turn on why your mother needs to grant any powers at all. Is she ill? Is she out of the country? Is her need for these appointments temporary or permanent? What functions does she really need to appoint attorneys in fact to accomplish? Would a trust agreemtnt be a better choice (for managing assets, for instance)?
Your mother should speak to an attorney, if she has any questions about what she really needs and why.
Mr. Philips is correct. To answer your question more directly though the answer is yes 2 people can have a poa for a person. There are pros and cons to having 2 people being a power of attorney. It can be drafted that both persons are required to exercise the power or one or the other. It depends on your mother's wishes. If you need one drafted your mother can call my office to assist. My Tampa number is 813-277-0800.