Herbie, I'm chiming in again because you're getting a lot of what not to do rather than answers to your question.
It's true that your wife won't know you're about to cross the finish line if she's sitting inside. But maybe she just wants to drive up early in case there are delays at the PP highway entrance gates, or catching the shuttle from Devil's Playground, etc. If she gets to the top quickly and knows there's at least an hour until you finish, why not have some donuts and hot chocolate and browse the gift shop for half an hour before going to sit outside?
I have 4 and 6 year old daughters, and my wife has come up to the top several years in a row with them to sit outside for about an hour and watch me finish. It's awesome for me and for them. I know my family's from high altitude. Still, if they stay hydrated, take it easy exertion-wise, and make sure everyone has a winter hat, winter jacket, and gloves, it should be a great experience. If it's sunny and not too windy, it can be really nice and they can shed layers, but at least have the layers with them.
Go for it! And yes, they can spend time in the Summit House if they want.