1)First, the good news: You may not have to rewrite your client server code (at least not completely)
2)This question may be better suited for serverfault
3)Get with your IT staff to discuss your needs. Developing the app without consulting them is asking for trouble, because they're going to be the ones to ensure the proper firewall ports are opened. Even if you had a VPN, without consulting them there's no guarantee it would even work. Because you would need
4)A routable IP address. Yes, DYNDNS or something similar would work, but that introduces another single point of failure. No IT staff? Then
5)Find an IT consultant knowledgeable in basic networking, or make heavy use of serverfault.