The answer will depend on your state's specific laws governing powers of attorney.
The general rule is that a person (principal) may appoint another person to act on the principal's behalf, by way of a document called a power of attorney. The person who holds the power of attorney and acts on the principal's behalf is called the attorney in fact.
Typically one can only obtain a power of attorney directly from the principal. So in your situation, it is unlikely that the Grandmother could give power of attorney to the 18-year-old to act on the Mother's behalf. Perhaps Mother's legal documents would permit the Grandmother to pass along the power, but that can only be known by reviewing the Mother's legal documents (if there are any) with an attorney.
It may be that you will need to take this in front of a judge to obtain the right for the 18-year-old to make decisions for his Mother. Judges have the ability to appoint guardianships, for example, so as to put someone's care into another person's hands.