My family lives in Shanghai (my wife is Chinese and we have 2 children 9 and 11) and our 4 cousins (aged 14-22) are arriving in Shanghai on 4 Aug and leaving Beijing on 16 Aug.

Any suggestions on itinerary?

My current plan is for all 8 of us to visit Shanghai, Beijing and maybe Nanjing and Xi'an during that time.

While in Beijing, we want to visit the Great Wall of China. Any suggestions for arranging a tour, given that there are 8 or us?

I recommend swapping in cooler (weather wise) mid points in favor of Nanjing/Xi'an because August is HOT in both places.

With 8 people, the economics of hiring a van to take you to the GW are quite good, and this will let you control the schedule. You'll probably even have space to bring along a guide if you desire.

Given the size of the party and the younger demographic, I'd set up something that is more balanced and not so city- and history-heavy. I would lose Xi'an and Nanjing, for starters, though not for the weather reasons moondog mentions. Xi'an is just too far of a geographic outlier and the younger set tends to find it less than fascinating. Nanjing is likewise a bit too history heavy. Instead, I'd get something small town and something active in there. My recommendation would be:
4th-6th Arrival and 2 days in Shanghai.
7th Morning get a van to take you and your stuff to Hangzhou. On the way, spend a half-day including lunch at water town either Wuzhen or Xitang. Mid-afternoon get to Hangzhou for overnight. Maybe see the Impressions West Lake show.
8th Hangzhou/West Lake in morning. Afternoon get van to Huangshan City (= Tunxi), can see the small old town there and overnight.
9th-10th. One day for trip to Mt. Huangshan, cable car up, hiking around, return to Huangshan City late afternoon. Second day for daytrip to the Yixian villages--I'd suggest Hongcun in the morning, Mukeng (requires hiking through cool bamboo forest) in midday), and Xidi in the afternoon, return to Huangshan City for overnight.
11th Getting to Beijing. Moving this many people is probably a job for the train. I'd get a van to take you to railhead at Nanjing South station (this will be about 4 hours by road) in the morning then catch one of the bullet trains leaving around 13:00. You'll be in Beijing by end of afternoon.
12-departure. Beijing. You need to allot 4 full days to this + your departure day.

Qingdao would be my personal pick to replace Nanjing/Xi'an with. It's really nice there in August.

I also thought of Qingdao but the Beer Festival is going on then--probably not the greatest of timings for this particular group.

I've been to Qingdao during beer fest twice and while the influx of visitors does push up hotel prices a bit, the overall impact on crowds is hardly a blip. Plus, beer fest is 5 miles north of the city. Finally, it is certainly worth checking out for the adults at least.

Weihai is a very nice coastal Shandong city as well and maybe not as overrun with visitors as Qingdao unfortunately tends to be in the hot season.

Dalian is not bad as well. The fallen one left a lasting tenure there, very clean and prospering city with a pleasant maritime feel and seafood in abundance.

Weihai's airport is closed so getting there is a real PITA. Dalian is quite pleasant, but it doesn't measure up to Qingdao in terms of overall appeal in my book. The trick to both is getting a bit out of town to some of the more relaxed coastal areas.

Yes, access seems to be via the industrial centre of Yantai. Still, a rather beautiful city I would recommend to anyone wishing to escape the summer heat in China. And the best seafood I've had in China, scoring over Dalian and Qingdao by a small margin.

Any advice on the latter? All of my Qingdao trips have essentially been for work, so walking the beaches only on a Chinese, hectic schedule.

This seems a good itinerary! Does anyone know who can arrange the van to transport us?

In the end, we decided to spend 3 days in Shanghai, spend a night in Hangzhou, where we saw West Lake, 2 nights in Nanjing and 7 nights in Beijing. We did all traveling by train.

We went to a relatively remote section of the Great Wall at Huanghuacheng, getting there by renting 2 taxis. The trip went well!