Is it permissible for a husband to tell his wife, "I will spend the night in your house," to prevent her from spending the night at her family's, and then spend the night at his other wife's house?

If the wife's family home is in the same town, and the husband permits her to go there, then her right to a fair division (of his time) is not forfeited, and the husband is obligated to make up for it if he goes to another wife. However, if her family home is at a distance that permits shortening prayers (qasr), and she travels there out of necessity with her husband's permission, then the madhhab (school of thought) holds that her right to the fair division and maintenance (nafaqa) is forfeited.