Hi Angel, Glad to hear from you! I think that it is wonderful that you plan on taking your mother to St. Vincent and the Grenadines, it is a lovely island group.
First of all where would you be flying from? Secondly, what sort of accomodations are you looking for if any?

St. Vincent's E.T Joshua Airport does not take international traffic so you would have to to fly into Barbados, St. Lucia or Grenada, then take an inter-island connecting flight on either LIAT or Caribbean Star.

A week is enough depending on what you want to do since these islands are not evry big. I am assuming that you have family living on the island so they can assist with the sightseeing.

Let me know exactly what the situation is and we can take it from there. Hope to hear from you soon.