What is the ruling on the third wife spending the night (with her husband) if only the second wife knows about the secret marriage, while the first wife is unaware and is expected to seek divorce upon finding out?

The default is the obligation of justice between wives regarding the night stay, and it is not permissible to favor one of them unless the others agree. Therefore, you are not allowed to favor the first wife in the division over the other two. Rather, you must divide equally among all three, unless the second and third wives agree that you divide one night for them and two nights for the first wife, in which case there is no objection to that.