The Shuttle by Frances Hodgson Burnett

Rosalie Vanderpoel, the daughter of an American multimillionaire marries an impoverished English baronet and goes to live in England. She all but loses contact with her family in America. Years later her younger sister Bettina, beautiful, intelligent and extremely rich, goes to England to find what has happened to her sister. She finds Rosalie shabby and dispirited, cowed by her husband's ill treatment. Bettina sets about to rectify matters. She meets Lord Mount Dunstan, an impoverished earl, who lives nearby and they fall in love, but he cannot speak because it would look as if he were after her money...This is a romance but it is also about the rejuvenating effects of Americans and American money on a somewhat decadent English aristocracy.