you could get (an old) mac mini (if you have the money left), and hang it on the wall there with a screen. You can then use it for cooking, watching tv, e-mail, but the best, you can do screensharing. The screen in the kitchen doesn't need to be the same resolution as the iMac.
I can monitor my 24" screen on my 13" macbook. Everything is just really small.
Anyway, that way you can see exactly what your daughter is doing.
But it will pretty obvious you're checking on your daughter.
btw, do you know about parental controls on the mac? Look into that too. I believe you can see any time you want what websites were visited. You can also block websites.