Could the battle over who knows best about taking care of family occur in part, because of me, but also sisters pent up sibling rivalry and jealously?

Yes...: Families are so interesting ...And complex. Old wounds, perceived wounds, guilt, jealousy, etc can all affect such a situation. If you refer to aging parents then hopefully they handled a lot with medical power of attorney so there should not be a lot of fighting. Family meetings/counseling could help air things out and lead to healing. Everyone hopefully has the best interest of family at heart.