Just an idea: jailbreak it and remove/rename the browser? The browser location is documented in the wiki
, so this should be a viable way of removing/disabling browser functionality. This would still keep over-the-air-delivery of content available.
I think it should also be able to simply prevent startup of the wifi itself (probably by removing a corresponding init script from /etc/upstart, but i can't verify this right now).
 ... at first. After a few weeks it might become a viable way of creating interest in ssh, linux and creative use of technology in your daughter while she tries to get the browser to work again. Which would be a good thing, too.
 Of course  also applies here.