In Portrait of the artist as a young man, Stephen evolves in many ways as he grows up. His mother represents the mold that he is breaking. I found her few appearances to be very telling of Stephen's character. Her first real involvement is at the dinner when the argument breaks out. She largely acts as the arbiter and tries to retain order. I believe this is one of the things Stephen internalizes and it definitely sets a precedence for he order-driven motives in the novel.
Later on, we get descriptions of how Mrs. Dedalus is the strict catholic that has hopes for Stephen to enter priest hood when she sends him to the boarding schools. We see this reinforced when she appears disappointed with his interest in college. This provides a perfect opportunity for Stephen to grow as a person beyond what his mother expects, expressing his individuality. By the time he refuses to go to church, he is far from the devoted boy from the beginning. Cranley points out how Stephen is now beyond acting under his mother's love, another symbol of independence. I think she is important, as both a static character and one of the only women exclusively portrayed realistically.
I do not envy Stephen's complete detachment from his mother, but I think it is a very significant detain.