Does anyone have any suggestions about a good, private driver for a small group (4 people) who would like to tour Copenhagen for 4-5 hours? One person in the group has difficulty walking long distances, so a driver might be the best option for us.
That might be problematic. Copenhagen is one of the least car-friendly cities I've ever visited. Can the person with mobility problems ride a bicycle? That would be a better method of getting around the city than by car. The issue is that many of the city's highlights are recessed away from traffic (like Rosenborg Slot, Nyhavn, Amalienborg, etc) and parking is very scant.
You might research the Hop On Hop Off kind of tour. It takes about an hour to drive by all the major sights. You could decide on that 1st lap what you want to see close up, then get off and on to see those things the 2nd time around. I don't know about Copenhagen specifically, but those busses may be allowed to go to some places a car can't or to get closer to them than a car can. My husband and I have really enjoyed the boat tours so many cities have. That might also be a possibility for your group. Google Copenhagen tours and you will find a lot of options that might suit your needs and maybe even some that could provide a tour guide driver combo.
Good luck. Here is another option you might try: http://www.go-segway.dk/?___store=en
Or this :-) http://www.stromma.dk/en/Home/