1. The Ewell children only came to school on the first day because he Ewells don't respect school or authority in his family. The had the reputation as lazy, incompetent , and constantly breaking rules/law. The head of the Ewell family intended to keep the reputation by keeping his children away from correct paths like that taken by other respectable families.
2. Many maycomb children need to stay at home because they are needed to work at home because of the Depression.
The maycomb families run a small farm that help them survive in the city. During the depression, they couldn't afford to hire another workers so the children need to get home and help their parents.