On the surface, the relationship between Laurie and his parents seems quite typical. When he starts kindergarten, he starts wearing jeans instead of overalls and this shows how he is becoming more independent. He begins taking a more active role in who he is. Laurie uses this stage of his development to try different things. The narrator (mother) notes how he becomes more thoughtless and insolent when talking with his father. Laurie is testing the limits of what he can and can not get away with. Laurie tests his parents' and teacher's patience. While this is also a typical phase that many children go through, it does seem that Laurie goes a bit too far. Laurie knows this as well. That's why he creates an alter-ego in order to do the things that he knows are wrong. On the other hand, he also attributes his good deeds with Charles. Note that it is Charles who acts as the teacher's helper. By acting out, via Charles, Laurie creates a problem in his relationship with his parents. He uses a lie (not telling them that he is Charles) in order to tell the truth.
The relationship between Laurie and his parents is troublesome because Laurie lies about what he has been doing at school and he is rude to his parents. On the other hand, Laurie tells them everything he does; he just uses his alter-ego as a way of disclosing everything. Their relationship would best be described as complicated or problematic. He tells them everything Charles does but does not tell them that he is Charles. So, it is an odd paradox of lies and truth. Their relationship is therefore paradoxically healthy but also problematic.