VNC, VNC, VNC. Two possible solutions come to mind.

1. Set up a VNC server on your client's computer(s). Set up their router to allow incoming VNC. Set up something on their network to update a dynamic DNS service so you can have access to it. (Assuming they don't have a static IP, of course.) This has the implication that you could potentially spy on them.
   
   
2. VNC can also be set up so that the "server" can contact the "client". You can give your client instructions on how to connect back to your computer. This way you can't spy on them.

The main problem with any of this is that once you have a reliable remote connection to their computers, all of the problems that they experience will become network problems.