Ash,
It does rather sound as if you need to use Remote Desktop/Terminal Services (Or any of a number of other similar utilities - PC Anywhere, etc.)
The first thing you will need is an account with permissions that allow you to access the customer's machine via T/S and you will need permissions to run the app.
Modifying the app may be a little difficult if your customer does not have VFP installed on that machine.
You could use a VPN connection into your customer's computer to modify the app. You will need an account with DialIn permission on the customer's machine to do this. Be advised - modifying an app on the customer's machine via VPN is fantastically slow but it can be done. You are probably better off modifying it on your machine and then you can simply upload the resulting report/exe, etc. (Doing it this way, the customer does not need to have VFP installed on his machine.)