Mrs. Doggie Daddy is the mysterious mother of Augie Doggie.
She never appeared within the series however in the episode "Growing, Growing, Gone" There maybe a clue about her.
There were few female characters in the Augie Doggie cartoons. The next door neighbour in "Treasure Jest" was one. There was the librarian in "It's a Worm Day.", then there's Peggy Poodle. She’s a friendly character who offers to share her lollypop with Augie and tells him she likes him. Augie responds by running as fast as he can for home to get away from her. "Dat’s my who’s growin’ up," Daddy cheerfully tells the Viewers in response. So It's probably concluded that Doggie Daddy ran away from his wife years ago and took Augie with him.