My sympathies were with you until I looked at the photos ... now I kinda side with your wife. That is one pretty place.
Our wives must be sisters. We have a slope that runs down to our gate that someone, at sometime "naturized" with daffodils and narcissii (?). In early spring, I must admit, it does look pretty but I'm not allowed to mow until they have finished flowering and died back. By the time that happens I also have a bumper crop of weeds in that area that run to seed and spread all over the rest of the yard. I spend the rest of the year fighting back but it is a tough struggle that I don't always win. When I try to explain the situation to her every year I'm greeted with an expression that says, "So????????". I've tried transplanting them but after 7 years I can't see that I've made any difference except now I can't weed-eat along the fenceline until they die back as well.
Sometimes you can't win for losing.
If my flowers were in the pasture and not in the front yard I think I'd sit outside in the morning with my coffee and just enjoy the view. Sorry but that's another vote for your wife.