These are the relationships Granny Jojo has with other characters in the series.
Richard is her son. They both have a good relationship as Joanna is very protective of him as seen in "The Authority." So much that she could not let him think for himself leading him to his current mind stature. She and Richard also have fights as seen in "The Man" as she is forbidden by him to see Louie. Later they reconcile when Richard says he is afraid of "losing" her to Louie, and she shows her affection for him.
Jojo and Nicole have a rather strained relationship. They often fight a lot like the average mother-in-law and wife, and this is seen in "The Authority." But this changes in "The Man" when she says that Nicole is looking "average," which shocks her. Nicole later supports Granny Jojo and Louie's relationship.
She loves Gumball as a grandson. Granny Jojo has actually kissed Gumball before in "The Kiss" when she was about to kiss him on the cheek but he accidentally turned his head causing the kiss to occur. She also teaches him about safety in "The Authority" and made him into the stature that Richard has. They interact again in "The Man" when Granny Jojo attempts to tell her grandson how true love feels. In order to make her stop, Gumball agrees to help her.
She and Darwin don't interact that much, but she accepts him like one of his grandchildren as seen in "The Authority" as she is trying to teach him about safety but takes control over his life and turned him into Richard. Again, they interact when Darwin helps her in "The Man" first by making her look more beautiful (although her look scares Gumball after, to which he and Anais agree) and then helping her unit with Louie.
She loved her ex-husband very much but he felt otherwise, and one day he abandoned her and Richard as stated in "The Man." In "The Signature," she speaks rather poorly of him, calling him "a con man and a shyster."
Louie is her new boyfriend as seen in "The Man". She is deeply in love with him, as they are always kissing. She even tries climbing out of a window to go on a date with him. They often kiss affectionately and in a gross way. As of "The Signature", he is her husband.