Hi. TechTV recently did a review on some products to help with this sort of thing. Here's a
LINK to the article. Look around, there are some decent products out there. One looks just like a USB "Jump Drive" but it acts as a lock for the computer. The computer is 100% functional with the usb drive in it, but when removed can disable things like IE or IM (this can be set by a parent).
Another system uses a credit-card type system where the parent can put a time limit on a card and the child has to swipe the card to use the internet, once the time limit is up the child is cut off and cannot get back on until the parent has put more time on the card.
I think a third-party device/software would be best in this situation because trying to disable or remove IE would be more trouble that it's worth. Oh, and Internet Explorer and the Explorer that Windows runs on are two different things, but IE is still integrated into the OS and would be a pain to remove/disable at will.