Both browsers can coexist. Why force a change? Make both available to the woman and let her choose. There are some streaming Windows media that will require either the WMP or IE.
I'll never go back to IE if for no other reason than Adblock and User Agent Switch plugins. Blocking ads makes surfing much faster and safer and faking off your machine, browser and OS makes it possible to get in places that would otherwise not let you in. Plus if a site is hacking at users with hijack attempts they may try the wrong hack if you pretend to be a different piece of hardware or OS or browser.
One of the biggest pluses for FF is the Flashblock plugin. Flash is so destructive and intrusive (to your network traffic as well as the individual computer) that you could show her some sites in FF with FlashBlock and in IE without and let her see how much easier it is to navigate otherwise "bad" sites. Try going to
www.ehowa.com without Flashblock and see what happens.
Firefox also lets you delete cache, cookies and history on the fly. To truly hide your tracks in IE requires a reboot and knowledge of hidden files in Windows.
You can't remove IE, anyway, in Win98 or ME without breaking many programs because they make hard calls to IE to render graphics. I used IERadicator in ME and had to replace some programs and remove and not replace others. But I like the stability and security that it put into ME not having any .com objects.
You can recompile XP using NetFrame and a utility from Nuhi. I removed the html rendering engine from XP Pro and it works fine without it except for the same issues as in Win98 and ME above. Removing the html engine completely disables the "Out-Of-Box-Experience" which is great for a home hacker, but not legal for a business, since your cd key doesn't affect the OS anymore. You can rearrange the hardware as much as you like that way and even modify the OOBE timer value without crashing XP.
If you use MS Office you will have to leave IE in. Open Office is an excellent replacement, but if your clients send docs in MS Office format, then you should leave at least one box running IE and MSOffice to open and convert the document to something more universal.
Firefox uses more memory than IE and is slower to load, but I still use FF almost exclusively. FF will ignore mime types and IE won't (Opera will if you tell it to).
By selectively ignoring certain file associations you can save files that would otherwise only stream. But you may have to remove certain plugins to make that work. Quicktime and iTunes on a Mac will not behave even with FF, so I deleted iTunes completely and deleted the QT plugin. I left the Real Media plugin and capture RM sounds with Wiretap because there is no free Real Audio to mp3 converter that is free.
Sorry for going on so long. The short answer is FF is for people who think and IE is for people who don't and don't want to.