In California can a son or daughter with a Power of Attorney, but no legal experience, represent a parent with dementia against another sibling in an elder abuse restraining order hearing? Also, can the one with Power of Attorney file the request for a restraining order on their parent's behalf?
A Power of Attorney allows acting on financial matters, not legal ones
The correct instrument for acting in the legal position of a person is guardianship. Guardianship does not exist for competent adults. For incompetent adults it must be applied for, otherwise the state has legal guardianship.
A court may allow a relative to act but that is entirely discretionary.
A power of attorney would authorize the agent under the power to retain counsel to prosecute litigation for the benefit of the principal (assuming that the grant of authority under the power is sufficiently broad), and to provide guidance to counsel on behalf of the principal in connection with that litigation. I've served as a lawyer in this situation in the past.
But it would not authorize the agent under the power of attorney to represent the principal without a lawyer, which would constitute the unauthorized practice of law (unless that agent is also admitted to the practice of law).