That might be an explanation for killing the mother, what about the adults at the school? And most of all why the children? What possible role could they have had in his life? I can not think of any.
This person was just an evil murderous depraved monster.
Possibly his mother discussed with Adam that she thought it was time for him to get on with his life, get a job and that she had discussed this with the adults at the school.
Now he is in a RAGE knowing that she discussed HIM with the outside world. The children may have been just a convenient defenseless afterthought in that rage, as he knew his mother loved those children. Jealousy and Hate?