Early 20th century. Similar in tone to Winter Cottage, Railway Children, A Lemon and a Star, The Melendy series, The Great Brain, Half Magic. A mother (widow?) and her children are trying to make ends meet in Connecticut(?). There's a scene in which the eldest son loses money he's supposed to use to buy coal, and another where one of the sisters befriends an elderly neighbor and they put on a play.
Any ideas?