Well of course the O/P may wish to correct my impression however what i gathered from the post is that for whatever the reason she does NOT wish to use another browser for her "business" accounts other than IE. So whether they work in Firefox is not relevant in this instance as i believe she feels she MUST use IE.
She said she can't use Firefox for the business sites because those sites won't display correctly in Firefox. That's the issue, not simply that she "feels she MUST use IE."
I have never heard of Opera but will try that. Do you have recommendations regarding this browser?
I use Opera a lot and sign on to my Allstate Insurance account, bank account, etc., with it, but I can't guarantee it will work with the insurance site you mentioned since such browser incompatibility issues do still arise. However, I do believe the problem of browsers other than IE not working with certain financial websites has diminished as IE has lost the dominance over the web browser arena it once had and, consequently, web developers are more prone to make their sites compatible with other browsers.