There is no UFT company to get an upgrade from. And the upgrades have nothing to do with which operating system you are trying to use it with.
UFT 2. cannot be upgraded on line. I think you have to have at least v. 5 to upgrade.
The only way to tell what version you are buying (if it isn't 3.) is to buy it and install it. Open the program, click the help button, slide down to About . . . and read what it tells you. That is a lot of bother for a dead program.
The 3.0 box is the only UFT package that actually said on the outside which version.
Every version of UFT has bugs. Some worse than others. 2.5, 2.8, 3.0, 3.01 were all pretty safe.
UFT 2. should run on Windows ME. Roots III won't run on Win 2000 because it needs a particular kind of DOS memory the Win 2000 doesn't deal with. But that is NOT your problem. Actually, v. 2. was mostly just a renamed version of Roots IV.
The Master Genealogist can import your UFT data from 2. or any version, even from a backup disk. TMG has a uility called GenBridge that will import without losing anything important. GEDCOM will not do that. Don't use GEDCOM.
Some things you and your mother need to decide are :
Any new program will require learning how to use it. There are many similarities between UFT or TMG. Who is going to try to use this program? You or mother?
If mother, can she handle the frustrations of learning a new program? Learning TMG, after using UFT, does take several months, even though they are similar programs. I am very glad I did made the change.
I assume you or your mother have one or more backups of the project data on some form outside the old computer, floppy, zip disk, tape?
Have you or your mother printed out the information that is still in the old computer UFT? There are several reports to choose from in UFT. It never hurts to have a hard copy backup.
About how many individuals are in her UFT project?