Simply make the webcam access area password-protected for registered users. You should charge for this service anyway.
I'm not sure about the webcasting, but I do a lot of remote wireless cam stuff with RC helicopters. :-) Look up the SecurityMan Air Watch, it's wireless, cheap (1-cam units $30 - $50 eBay, retail $99,) supports color and sound and the receiver has an auto-cycling function that swaps between up to 4 channels. The output is standard RCA jack video and audio output. For power you just need 800 mah/9 volt adapters for the cams and the receiver (comes with them.) I use two tiny 800 mah lipos in series for my helicams. :-D
With one of those in hand, all you'd have to figure out is a) do you have video input? If not, you need a card that will cost you $50-$200 to accept video in, and b) software to digitize and webcast the video from a computer. You can probably use any webcam software for this purpose, but you'd better have a hosting service that won't break the bank - live video feeds take up a lot of bandwidth.
Hunt around for articles on webcasting.
The other alternative is to look around for teen/children activity sites. One example I have seen is a roller skating rink that webcasts during open hours. Parents can log in and see if their kids are still at the rink.
You should have no legal problems if it's openly advertised and in the agreement when the parents open an account with a daycare facitity, and better yet if the service is passowrd-protected. In fact, most parents will appreciate it.