No one ever said your mother was named for Venice. Most people named
Venetia or Venecia are probably not named for Venice, either. After all, I'm sure all those people naming their daughters
Mackenzie are not naming them that with "son of
Coinneach" in mind. They, just like your grandmother, liked the sound of the name without any thought of the meaning.
If you want a real meaning, the meaning of Venecia is the closest thing. Since your grandmother MADE UP the name, then the meaning of the name should technically be the combined meanings of Vanetta and
Alicia, and asking about the meaning of the made up name Vanecia is pointless.