The install process, I don't believe, allows you to select the directory. I just can't remember but here is what I'd suggest.
The Que really wants the default directory structure so I'd unistall everything. Delete the registry entries for the Palm, PalmDesktop and all related Palm type keys.
Reinstall the Que with it's default path's.
Then install the T3's Desktop and see if you can change the directory path's during the install.
The reason you'll have to unistall everything is that WinXP will sense the directory structure and not allow you to change it if the registry entries are still there.
You could partition the hard drive and install one on drive C and the other on drive D for example.
If the T3's install will allow you to choose a directory then you should be ok because the support files are all contained within the selected directory.
Give it a try?