Your wife is correct. Our lanai faces NE it would be a dealbreaker to have it facing another direction.

When you have guests over it will always be in the afternoon or evening. This is why the east or north facing lanai is the best location. The shade is always welcome when you entertain.

Words of Wisdom
 

That seems to always be the safest bet…lol

Should not be a deal braker. There are more important factors. I've come to love my WSW facing lanai.

My first Villages house had a northeast facing lanai with an east facing pool. I hated it. The southwest garage got all the sun and would heat up to 130+ degrees - I measured it. At the height of summer, I could feel the trim in the car starting to melt. The house seemed dark all the time. The house would block the sun from the pool starting at 3 pm, just about the time I wanted to swim.

I built a new house two years ago and chose a lot with a south facing lanai. I get morning sun in the master, to help me wake up and afternoon sun in the kitchen, when I'm working in there. The lanai is about double the usual depth. I only get sun into the lanai after about 5 pm because the sun is high in the sky most of the day and going over the roof. It doesn't shine under the roof like in Michigan. The garage is north facing and is much cooler. My neighbor is on their fourth house and chose the same orientation as I did so that the sun is over their pool all day.

Another issue to consider is that a north facing lanai will give you a south facing front yard, with nothing to shade the lawn. The sun beats down on the lawn all day and injures the grass.