These possibilities do not depend on your parents' marital status.
In a power of attorney, one person names another person as his or her agent"”usually to act if he or
she becomes unable to makes decisions alone. No one has the right to make the appointment for another person. So, for example, your mother would always have the right to appoint her own agent; your father could never do it for her, whether they were married, divorced or separated.
There are no automatic appointments in a legal guardianship or conservatorship, either. In these proceedings, someone petitions a court"”usually the local probate court"”to appoint a person to make decisions for an incapacitated person. A judge then makes the appointment based on the person's best interests; if a qualified family member is able and willing to do the job, that person will usually prevail. For more on this, see Caring.com's articles and explanations at www.caring.com/adult-guardianship.
And since you seem concerned about potential complications with your parents' wishes, it might be an ideal time for you to share this information with them"”and encourage them both to get their wishes documented by finalizing their own powers of attorney and other estate planning documents.