NO a power of attorney cannot act after death. If there cannot come to agreement you can petition the court to let the judge make the decision after a hearing.
In the ideal situation, the decedent would have specified a preference in some document - typical choices are a Will or a Healthcare Directive. Otherwise, it is left to the surviving family to come to some decision.
While hiring an attorney and heading to court to ask a Judge to make the final decision is always an option, it is far better for future family relations if the family members can come to an agreement by themselves. If you feel that this situation cannot be resolved without the intervention of some third party, you might want to look into mediation rather than litigation. A good mediator can help guide a discussion of the issue and help you to reach a mutually satisfactory resolution.
The proceeding is simply for informational purposes. It does not create an attorney-client relationship.