Is Aphrodite a grandfather or great grandfather?

Neither, she is a Greek goddess, but yes, her son Eros lay with Psyche and her grand daughter Hêdonê was of that union.

Harmonia, who was the daughter of Aphrodite, had with the mortal Kadmos both Semele (from whom Dionysos is called her son) and became the goddess Thyone; and Ino who with her son Melikertes became the sea deities Leucothea and Palaemon.

In that case, by Semele, grand daughter of Aphrodite, Dionysus would be Aphrodite's great grandson.