OK, I went back to try the Screen Sharing thing, again. Mainly because I read somewhere that there is actually a "Screen Sharing" app. I finally found it in /System/Library/Core Services. Of course, it's the app that does all the work when one clicks the "Share Screen..." button in a Finder window.
Clicking the "Share Screen..." button is the only way any normal person would use the "Screen Sharing app, in my opinion. I'm not sure why anyone would search through the System files for the actual app. And clicking the button is how I pulled up my wife's MBP screen just now, exactly how I did it last week.
HOWEVER, it simply opened a window with her screen, just like it used to this time! What?!
That's right, no putting the window in a "space" of its own! Everything is exactly like it used to be in Leopard/Snow Leopard! Except for the ability to use the Full-Screen option, of course. I checked the app's menu and they look the same. And, of course, the menus are fully available because all the other menus of whatever is running are still there, no putting with Spaces at all.
How or why the window opened in Spaces last week is a mystery and one I hope to never need to solve again.
OTOH, it may be a new Lion feature: Shared screens open either in Spaces or a normal window depending on the day of the week or whether it is an odd or even day of the month. Makes as much sense to me as opening the shared screen in Spaces...