Depends on the design of the polo and the rest of the clothes you are wearing. If you've got particularly neat and traditional style then I guess it makes sense to tuck in. If you're wearing a more modern cut polo then it could go either way and it does depend on what you're wearing with it. I prefer untucked myself but I always make sure the polo's look new, clean and fresh (must be ironed) so it doesn't look sloppy. Get polo's that fit you well too, they shouldn't be baggy or skin tight.
At the end of the day though why not make your wife happy and leave it out? They are usually designed to be worn untucked anyway.