Should a child be changed to a different class after the beginning of school and the homerooms have been assigned? I say yes and no. I will explain both of my answers in more detail below.
When a child begins having trouble in school, it is not unusual for the parents to first blame the teacher. Next they usually blame the other students. They suggest that either the teacher is picking on their child or that the other students are a bad influence. Either way, the thought of taking their child out of the class and moving him/her to a different class can come up in conversation.
In some cases a child should be moved. If another child is threatening or bullying, a move might be an option. In other situations, a child may not be best in class where the child and teacher know each other well, such as family friends or relatives. The same may be true with classmates. Cousins, brother, sisters, etc. may not be suitable to be in the same classroom. However, this is rarely the case.
In most cases, the child is misbehaving on his/her own will. It is very likely that the child would have trouble no matter which class he/she is part of. I feel that in these cases, the child should be the focus of the conversation and not the teacher or the classmates.
I have found through teaching that some children are best separated in the classroom. However, this would be true with every classroom setting. I have also found that there are personality clashes between teachers and students. Some students prefer a teacher more than others prefer him/her. However, that is part of life and something that children will need to learn to accept and deal with. If the teacher is being fair and honest then the child needs to be taught how to get along with various persons.