We are building a web app as solution #1, but eventually want to supplement it with a mobile application, but I'm unclear as to when you leverage mobile frameworks (i.e. Titanium, PhoneGap, etc) are you simply adding a mobile-compatible layer that communicates with the core of web app? In other words, will the core (all of my classes, logic, etc) still serve to power the mobile app? Or do I have to write a completely separate mobile app (logic and all)? I'm using MVC for the web app, so I'm hoping I can reuse as much of the MC as possible and just leverage a mobile framework for the V. All thoughts/assistance are greatly appreciated. Thanks!
Yes you can reuse your logic from webapp to your mobile app.
You say you are following MVC then as per I think you can reuse most of Model and Controller logic only view is the thing which is going to be changed.