Your wife is correct. As a one time thing perhaps. But to spend 50 minutes alone in a car giving a ride to someone else’s wife every day for the next ?? Years is just a really bad idea.
But I have a better idea. You say both of you are married. So this is “shidduch crisis neutral,”. Why not both get divorced; you marry her and her husband marries your wife? Much more convenient since then you can commute with your wife! (That’s what this is headed towards anyway)