The Family Potter arrives only a little late (because punctuality and small children don't go well together). They have with them Harry, Harry's portable bassinet for his afternoon kip, Harry's nappy bag, Harry's toy bag, and--more pertinently--Lily's prepared-for-anything Order-first-aid supply kit.
Lily is not flying. Lily is on the record as having stated that the best thing about graduating from Hogwarts was that she never had to get on a broom again in her life. James can represent the family honour.