Do I need to have my child do the same homework and assignments as the other children?

Not necessarily the same. In common: the purpose of homework isn't "doing the same amount as everyone" but learning and retention suited to the child. Adjusting the amount or content (reducing, easing, replacing with a life task) is widely done as reasonable accommodation. What the family decides: how much to insist on "the same as everyone" is your choice, based on the child's burden and your views. A guide: "does the task suit the child's ability?" "is the family being worn down?" Share the purpose with the teacher and discuss the amount and form on the premise that "it doesn't have to be the same."