One of my biggest worries with a *2 year old would be online predators. A *2 year old may think she is smarter than her parents, but that usually isn't so. Predators are very good at what they do.
I would install something like Spector Pro on the home computer. [url]http://www.spectorsoft.com/[/url] She will log on eventually.
If she is going online somewhere else, monitoring another computer without permission is illegal.
