Well yea, Oba-sama does not make SessMama sound as old as Obaa-sama, but then again, Oba-sama would be closer to "aunt" where as Obaa-sama properly translates to "grandmother". So the meaning would be inaccurate for Oba-sama.
But I still think it's well justified to call her 'grandmother', after all in Japan people are often addressed according to their titles, and SessMama's "title" in the pup's point of view would be grandmother.
And especially if they don't have that much interaction, "grandmother" could be used as it properly depicts their relationship to each other, but does not imply as much affection or closeness as the many variations of the word, like grandma.