Is reciting the Qur'an and legitimate ruqyah over a sick mother, and blowing into the right hand then wiping her body with it, a sound practice?

What the questioner is doing is correct, if the book contains legitimate supplications and invocations. In Sahih Muslim: "There is no harm in ruqyah as long as it does not involve shirk." And from Aisha: "That the Messenger of Allah, peace and blessings be upon him, when he complained [of an ailment], would blow upon himself with the Mu'awwidhat (Surahs Al-Falaq and An-Nas)." So, continue with the ruqyah, and make many supplications for her recovery.