Vyse's Mother is a minor character. As her name implies, she is the mother of Vyse and is Dyne's wife. She was also Aika's foster mother after the death of her parents until she was old enough to take care of herself.
Her actual name is never mentioned in either the English or Japanese versions of the game.
Before Vyse and Aika go get the Moonstone on Shrine Island. If you talk to her she will give you a couple Sacres Crystals.