Arnold had a conflicted relationship with his mother, both revering her as a wonderful woman who was "very prim, very proper" ("Polymorph"), but also hating her for being so strict and uncaring, referring to her as "A bitch queen from hell" ("The Inquisitor").
Mrs. Rimmer had a reputation for being very free with her affections. Despite being married to Arnold's strict disciplinarian father, or perhaps because of it, she was known to have had affairs with Porky Roebuck's father ("Queeg"), her brother-in-law Frank, Dennis the Gardener ("The Beginning"), and several other men. Arnold once mentioned that The Boys from the Dwarf could have his mother, since "Everyone else did" ("The Last Day").
When Arnold was seven years old, his mother told him that he was in danger of being held back one year at school (she did not seem very concerned by his being tied upside down to a tree during the conversation). She had been to see the headmaster to explain that she wanted Arnold to be a test pilot. Arnold was allowed to move up with the rest of his class. In another dimension, Arnold was held back and the humiliation caused him to become a stronger person - Ace Rimmer ("Dimension Jump").
When a Polymorph attacked Red Dwarf, it wanted to incite Arnold's anger, so transformed itself into an exact replica of his mother. She proceeded to sleep with Lister and taunted Rimmer with tales of their sexual exploits, causing Kryten to jeer at the prim, proper and austere image that Rimmer had given her. The mention of alphabetti spaghetti as a sexual aide was enough to tip Arnold over the edge, so that the polymorph could feed on his anger ("Ploymorph").
Rimmer's mother gave him the middle name of "Judas" because she was a member of the Church of Judas, which stated that Judas was the twin brother of Jesus Christ and took his place on the cross, allowing Jesus to return on the third day and later raise a family with Mary Magdalene in the south of France, as well as inventing the wheelbarrow ("Lemons"). She was also described as a Seventh Day Advent Hoppist due to a misprint in the Rimmer family Bible at 1 Corinthians 13:13 ("The Last Day").