It is difficult to say what would be the best approach given the limited information.
- Yes of course you can program against the serial port.
- Yes you can remotely access the desktop, often called running a headless RPI
But where to go from there?
- Perhaps start with the Windows version for RPi, it is a cutdown version for sure, but perhaps there is enough there for what you want. Also check out if there are any licensing issues
- use a different language for the RPi version, most likely Python
Or you could do what I did and switch development environment to XOJO, it is what VB 6 would be today if it had continued. Except that you can cross compile for Win, Mac, Linux and the RPi. You will not build the next version of Excel with it, but it is more than good enough to cover most business apps.