When you said you have a stop-over of 24 hours, I assume that you will have a hotel to spend 1 night. So your mission is to do some shopping and then see Mutianyu GW before heading to PEK.

Here is how I see the logistics, others can chime in.

I’d get a hotel in city center (say near Wangfujing, to be close to shopping). I’d do all my shopping post right there at Wangfujing, or else where by taxi. That would free up much more time the next day for the GW.

Most international brand hotels would have several private cars with drivers (they are usually not related to the hotel other than to have the permission to serve hotel guests) parked short distance outside the hotel. I would not hesitate to approach them and strike a deal. Do so after you’ve checked in that night. Reserve it for next morning. Language barrier can be a slight problem, but not serious. If possible, you can say Mutianyu Great Wall & airport they would understand. Tell driver (or give him a piece of hand written paper) exactly what time you want to start, and what time you want to be at the airport. I would skip dealing with the concierge of the hotel, unless you would not mind to pay more.

As for the time budget, reserve around 2 hours from city center to Mutianyu (I clocked my visit from center city was less than 2 hours without rush, only encountered a bit of slowing down among ring roads, not a problem). From GW to airport should be no more than 90 minutes. Of course the above are subject to traffic. Since GW-PEK would be so much outside the 4th Ring, I think 90 min should be safe. Other can comment since I have not done that.

Car & driver fee depends on what type of vehicle. Bimmer & MBZ tend to be mostly through the hotel concierge and could be expensive. I did not use them. I booked a Hyundai 4-D sedan with a driver, air-con & no smoking inside for 500 RMB (all toll if any included) just prior to 2008 Olympics. This was for Am in Mutianyu with a later afternoon stop at Summer Palace before dropping back to hotel.

Hope this could be used a guide. You should ask to check out the car when you first enquire.

I told driver that I would paid him at the end of trip. No problem. Oh, one more thing, if you don’t want to stop by gift shops post GW hikeing (such as jade factory etc…., tell the driver so before hand).

I would start the GW early and after the hike on the wall, you can have lunch down by the village area.

Your luggage would be fine. Do lock everything and note car license etc…e.g ask your daughter stand by the car and you take a picture of her & the car, showing details of then plate.

Have a great trip.