You allow the babysitter to use your computer? And you allow her to close a program that you want running? It would be easier to tell her not to tamper with any programs that you have running. Ideally, for virus/malware purposes, it would be really smart to not allow her to use the computer at all...especially under your user account, which I'm assuming has admin priveledges.
That aside, this information might help you (if you have a Windows PC). I'm not a Mac computer person, so I can't help you with a Mac.
Create an account on your computer for the babysitter (without admin priveledges) or enable the guest account (preferred and easier). When you step away from your laptop, hold down the Windows key on the keyboard and hit the L key. This will lock your screen, leaving your account signed in. Now the babysitter can login as a guest or under the account that you created for her. Since she is not an admin, she won't be able to close the icamsource program...at least not without rebooting the computer.
There are some programs out there that will allow you to run other programs in a hidden state (not show up in the system tray)...but I didn't see any free ones. There are ways to use some program scripts to hide icons on the system tray...but I think it just changes the icon to a blank image...meaning a user could still right-click on the blank area and shutdown icamsource. There is also a way to permanently change the task bar icon for the program, and you could rename the program itself to something like "audiomanager.exe"...just make sure you update any startup links to the new program name. Another thing to take into consideration...any user with appropriate permissions could use the task manager to kill icamsource.exe. The guest account should not be able to kill programs executed under another user, however.
Out of curiousity, are you using your laptop's webcam as the camera source? If you have an IP camera, you could run icamsource on any computer in the house with an Internet connection...it wouldn't need to be the laptop.
