Thank you. Then Mutianyu would be a better choice to do both?

Marginally.

Would be possible in half a day. But its just a renovated section, so no climbing and lots of tourist.

That's not entirely true. Mutianyu has plenty of steep sections once you get up there, even on the restored part, and if you walk away from the central tourist part of the wall by the cable car and chair lift, towards Jiankou, you can get to more unrestored parts and also lose most of the other people.

If you get an early start around 07:00 from central Beijing and get to Mutianyu about when it opens, you can have a fairly tourist-free experience for the first hour. Come down around 11:00-11:30 and have driver take you to Summer Palace east gate and drop you off. You won't go through central Beijing to do this. Assuming a quick lunch either at Mutianyu or near the Summer Palace, you should be able to hit the SP between 13:30 and 16:30 then exit the north gate and make your way to the subway to get back to center of town and wherever your hotel is. Or find an empty taxi if you can. Having the driver wait around for you and pick you up at another SP gate is possible but adds to the cost.

That was pretty much the plan, but with a 630AM pickup at Hilton Wangfujing. But the again, we've got for full days and one half day on arrival to explore Beijing--should I spread this out?

Yes but thats Jiankou and not Mutianyu. So it make more sense, if he is in hurry and want so see something of the old real part, to go to Jiankou and than walk to Mutianyu. In this way he will be able to see the old and new and get some steep walking.
He could drive to Xizhazhi and than walk up to Zhengbeilou, continue to Mutianyu. I did this last year.
Take a taxi to the red cross (Xizhazhi) then follow the blue line up to Zhengbeilou.

Summer Palace is a lot of walking (or can be) so you might consider doing that a separate day. We came back from Mutianyu to the Lama Temple. From there you can take Metro to Temple of Heaven, if you want, or some other place near the center of town. Then do summer palace some other morning (or afternoon).

She advised the poster in question to go to Mutianyu and walk towards Jiankou.

They will never get a taxi if they exit at Jiankou but its easy to get one at Mutianyu @:-)

She did not say "walk between the two"; she said "walk TOWARDS Jiankou". Based on my reading, this presumes a return to Mutianyu.

And this is why I recommend to start in Xizhazhi, otherwise they have to walk return on the same section which will give them just half of the possible experience, okay? I did that hike and I visited Mutianyu twice in the last two years, so I know the area.

I have hired a car and driver (recommended on this forum). So I can have him drop us off in one place and pick up at another.

I do not like the idea of driving 3 hours to the wall, so we will go with Mutianyu. How far is the walk you recommend from Xizhazhi to Mutianyu? Could the driver drop-off one and pick-up at the other?

Thanks.

Seems to be a long drive around. If you hired a car this is maybe not the best way, I would only do it with a taxi.
So just go to Mutianyu and walk to the left if you reached the top of the wall. I don't think you will reach the old part if you walk in this direction, there are some really steep section you have to pass. If you get it, it will be exhausting in this direction to walk up further on the old part. Walking down there is a lot easier.

I didn't realize you had 4.5 days but thought you had a 1-2 day visit only. With the time you have, spread this out. Do the GW (whatever section you choose) paired with a lower-intensity walking additional site in Beijing on one day, and pair the walk-intensive Summer Palace with another less taxing site on another day.

You're correct, I said walk TOWARD Jiankou...as in not the other direction. I think my description was pretty clear it was a go up and come down and Mutianyu, not a journey between wall sections. If the requestor wants to take the time and walk between two sections, that's his lookout. But that wasn't made clear in his first post. Take plenty of water.

Note that when planning to be dropped at one Wall section, particularly a sparsely-visited one, and picked up at another, make sure the driver understands precisely the what and when....particularly if you aren't a Mandarin speaker. And you must have a local-enabled phone and the driver's mobile number to communicate.

I walked both, up from Mutianyu and return there and also did it from Jiankou/Xizhazhi to Mutianyu. You did this both too jiejie? My advice should also be allowed here.
Going up from Mutianyu to Jiankou is more exhausting than to start in Xizhazhi. So they will need more time if they want to see the old parts. A lot people are not able to reach the small ticket office up the wall before the old part starts if they go in this direction because of the steep stairs. If you walk from Xizhazhi you have to climb up a hill, which is also steep but easier to walk than the stairs. In this way they will start at the top of the wall and then walk down to Mutianyu which is easier. The only problem was to find the wall from Xizhazhi direction. There was so much fog that day, that we couldnt saw more than 20 meters.
But this is not a really good option with a own car, its a long way around.