That browser uses Internet Explorer internally - it's just been repackaged, much the same as AOL does to their customers.
Have you tried logging off, clearing out both your cookies and cache completely (using Internet Explorer's method, since it's the same browser internally anyway), then logging back in?
As for your parents refusing to install Mozilla, well, there's still a solution to get around that

Get
Portable Firefox and extract that to some hidden folder of your choice, and use it from there - no installation technically needed. It's designed originally for putting on a USB key so you can use your same settings and the browser on any machine, including ones you can't install stuff on, but it works just as well in this instance too