There are a few different things that might be going through your head when you feel that heeling the boat is undesirable:
1) It's uncomfortable (you discovered that already)
2) It's inefficient (mentioned by previous posters)
3) Maybe the boat will turn over (which is maybe why you're scared)
When I take friends out for the first time in high winds, they inevitably ask, "Is it normal to be leaning over this far?" or something equivalent. I always tell them that it is basically not possible for the wind to capsize the boat. Most keelboats can be heeled more than 90 degrees (i.e. mast in the water) and the ballast will still cause the boat to right itself, like those stand-up punching bags with clowns on them. I just explain how stability in a keelboat works, and my guests go, "Oh... oh, okay." (You have to start worrying once the waves are more than twice your beam in height.)
My guests happy to know that I am confident that it will not be a problem, even if they're still a little scared
So that's for your edification. Let your wife know that heeling is perfectly safe. Explain to her that, for reasons mentioned in other posts, it's still not what you want to be doing if you can avoid it.