Certainly no one can tell you how to convince your wife. That is between the two of you and the family. How old are the kids? My oldest was on board at 5 days old and we lived aboard a Catalina 380 (with two dogs to boot!!).
Our Catalina 380 before a trip to the Tortugas
My wife and oldest at the wheel
Chase Watching TV 'Somewhere' in South Florida
I will tell you that some of the best memories of my life have been on a boat... and some of the worst. Living aboard is very tough... much more tough than living on land. I think it requires a high level of commitment starting off. You then get an eye opener afterwards because things just are not what you thought they might be. It certainly is not all sunsets and margaritas. And after you have spent many weeks/months aboard, 40 feet gets very cramped. You will find that you either have to become an anal retentive neat freak, or you will be tripping over crap everywhere. You will also have the storms, the concerns for lightning, the crappy marinas, and I should also mention that a very large percentage (I estimate close to 95%) of those that will be around you either have no kids or are very retired. We were by far the youngest people on our docks. THat creates difficulties for kids as there is no one their age. There is also a LOT of drinking at the docks. Some do it responsibly while others... well, let's just say you need some noisy fans and hatch covers.
I think the most frustrating thing is all the crap that breaks or runs out. Examples are ice (an absolute luxury on a boat that everyone takes for granted until they live aboard), or pumping out the head every week (with pumpouts that do not work half the time), or running out of propane in the middle of a meal, or having the air conditioner blowing full blast in the middle of summer and still being hot down below because the decks are 40000 degrees. The list goes on.
I am not telling you all of this to dissuade you from cruising and Living Aboard. I am telling you this because I have done it and it is different from than what is portrayed in the magazines. At least it was for us. You will either find a way to deal with it, or burn out quickly. That is also why I think all parties (wife AND kids) need to be "on board" for living aboard or it will be a miserable experience.
On the flip side, we are going to do it again and are gearing up just for that. We loved it so much (and are so passionate about it) that we bought another boat and talked my parents into doing the same.
Dinner aboard mom and Dad's Tayana 42
You will also learn to be closer as a family. You will learn to appreciate and enjoy the very simple things of life and the simplicity of living on the water. You will come to truly love sun sets and birds flying by. You will come to know (for better or worse) all you neighbors and call them friends like we as a country used to do 50 years ago. You will come to respect the life on land and all of its conveniences that everyone takes for granted. You will then come to realize how commercialized everything has become. And in the end, if you can take it long enough, you will come to learn yourself and respect the world around you. But it isn't easy. I dare say it is much more difficult then living on land.
But it was/is worth it - to us at least...
Mom and Chase before a casual dinner
Me watching the sun go down 120-130nm west of FL
Chase Steering our 400
Chase and Glen having fun
Me and the boys playing a game
Maybe it is sunsets and Margaritas after all??