If I've understood correctly there are two questions here.

The first is that you have a program that resides on a Unix machine and you would like to run it from a Windows workstation.

I'd recommend to use a software like VMWare. The only caveat is that if I'm not mistaken VMWare is a commercial (paid) software. A free one is VNC, but I don't know if you can run a server on a system and a client on another (probably not).

The second is about "mounting" a Unix filesystem on a Windows machine. I really encourage you to follow Grygonos's advice. Samba is a really great software and once is installed it runs smoothly.

Hope it helps.

Best regards,