Is it permissible for a woman observing 'iddah (waiting period) to take her son to school and pick him up if there is no provider or driver available?

It is permissible for you to take your son to school and pick him up from there, because a woman in her 'iddah (waiting period) is allowed to go out during the day for her needs, and what is mentioned in the question is considered a need that permits her going out.