Still, Bert, it seems like needless complexity -- I'm sure it can be done, but it is likely to fail when you need it most.
Depends on who needs to use the internet -- but the simplest thing would be just to get a second internet channel if they really have to be separated.
Anybody's cell phone can be wireless hot spot for the clinic staff.
Why not just plug an access point into the empty LAN sockets on his router for the laptop to get onto his network?