There is a slight difference between an impression Camus gives and an impression Meursault gives: one is the author and his impressions can only be inferred--if inference of author is at all possible--from indirect evidence in tone, irony, sarcasm and proximity to the narrative, while the other is a character whose impressions are more directly revealed as part of the objective of the narrative. Also, there is a slight difference between an impression about Madame's relationship with her son and an impression about Meursault's relationship with his mother: the first, who is dead and not a focus of interest, has a relationship that begins with her thoughts and feelings, while the other, who is the central focus, has a relationship that starts with him and his thoughts and feelings.
The best place to infer Madame's relationship with her son is at the vigil at "the home" she stays in. We know that she had seen her son only "seldom" for one year since, of the three years she had been at the home where she was cared for, he had mostly quit visiting during the last. We know that Meursault went seldom indeed during that last year since the caretaker had never met Meursault before, though he had looked into Meursault's background, income and career. We know that Madame Meursault, when living with him, watched her son a great deal, did not talk with him, and cried a good deal when she first went to the home. We know that Meursault was not a "companion" for his mother.
When we lived together, Mother was always watching me, but we hardly ever talked. During her first few weeks at the Home she used to cry a good deal. But that was only because she hadn't settled down. After a month or two she'd have cried if she'd been told to leave the Home. Because this, too, would have been a wrench. That was why, during the last year, I seldom went to see her.
From this, we can infer that Madame Meursault did not understand her son (watching him without talking) yet loved her son (crying at the separation). It may be inferred that she probably did not understand her son and was puzzled by him and worried about him. Now the question is, what is Camus impression as opposed to the narrator's impression, if that is truly what you are asking for: the impression of the author as opposed to the impression of the first person narrator, who is Meursault himself.
If it is at all possible to do, how do we separate the author from the narrator? Here the tone doesn't help because the narrator is the principal character: the narration is an interior account of events. Irony, sarcasm and proximity will be less than helpful for the same reason. One thing we can draw upon is characterization, which is strictly a reflection of the author's impressions. From the beginning, Camus characterizes Meursault as confused, as feeling the need to make excuses for himself, as being easily embarrassed by himself and as a bit hectic and disorganized, lacking in foresight.
- "Mother died today. Or, maybe, yesterday; I can't be sure."
- "Afterwards it struck me I needn't have said that. I had no reason to excuse myself;...."
- "It was something of a rush, getting away, as at the last moment I had to call in at Emmanuel's place ...."
- "I had to run to catch the bus. I suppose it was my hurrying like that ...."
From this and with this in combination with what we know about Meursault's mother, I'd say that we can infer that Camus' impression of Madame's relationship with her son was that it was a disappointed and concerned one; one in which she felt sure that she or the world had failed him but in which she could not understand how or why or who or what had failed. I'd say the impression Camus gives is that it is a relationship that she weeps for because she dreamed it would be something entirely different from what it was.
Mersault seems to maintain a very similar dispassionate emotional distance from his mother as he does with the other characters in the story. He does not cry at her funeral and the lack of emotion he shows at the funeral is used against him at his trial to prove that he is an unfeeling, rather inhuman person. (It is, in effect, Mersault's lack of humanity that is used to condemn him to death: "Meursault is convicted as much for his psychological indifference, his selfish and asocial behavior, and his lack of mourning for his mother, as for his crime" (eNotes).)
Despite the accusations against him regarding a lack of emotional attachment to his mother, Mersault repeatedly mentions her and eventually Maman becomes a recurrent character and motif in the novel. In her distance from Mersault, she is inscrutable and serves as a parallel to Mersault's own inscrutability. In the end, he feels that he finally understands her and understands why she would want to start life all over again with a new fiance (when she is already so close to death).
Yet in coming to this understanding and in identifying himself with Maman, Mersault thinks that "Nobody, nobody had the right to cry over her." Simply put, Maman is a separate person and Mersault believes that people "own" their own emotional and psychological lives and have no right to trespass on those of others. This is the crux of what Mersault tells the prosecuting attorney and what seems to enrage him when he speaks with the priest.