Ramblings from the Creator of WilsonDotNet.com
You mean you haven't changed your default browser to Firefox yet?!?!?! Have you got the developer extension for it? It's Fantastic! (Plus the ctrl-T and Ctrl-F buttons).T.
I once had to switch from IE to Firefox to sign up for a section of Microsoft.com. It was a passport-enabled site (I think the ISV or partners area, if I remember correctly). Very strange.
Today
I recently switched to Firefox on my Mac, but unfortunately there is a bit of a nasty keyboard bug which locks the keyboard within the browser - so my daughter is still on Safari atm. I am full time on Firefox for Windows though (except via SharpReader :( ).
Get the IEView plugin as well. It will add an "Open this page with IE" menu item to the right-click context menu.
Don't hold your breath hoping that FireFox will fix your problems on kids sites -- these are usually related to the Flash player itself. Better luck if you re-install the player.