Is there a way I could connect to my children's computer so that I could see what they're doing?
Net Nanny is perfect, it's got parental controls, swear masking, safety mode for youtube and google, and it has literally no weaknesses. Bad news is it costs money!
The easiest way is to use OpenDNS Parental Controls. Sign up for an account on their website and use the DNS addresses. As soon as the network will be added to OpenDNS you will have the possibility to apply blocking filters to their connection from the webpage without interacting with their computer or devices.