People have mostly got this explained before me, so I'll add what I know of how they're styled. Upon investment as such, Mortimer would be styled "The Prince Mortimer, The Prince of Wales." His wife would be "The Princess Hortense, The Princess of Wales," and his son would be "Prince Edgar of Wales." So while not *the* Prince of Wales, his father's investment makes Edgar "of Wales."

Should Mortimer die before becoming king, Hortense retains the right to use the title she held while he was alive, with "dowager" appended. So she would be "The Princess Hortense, The Dowager Princess of Wales."