Who am I to tell you how to raise your kids? However I cannot resist the line, "kids will be bored with museums ." If you are in China, it is the perfect time to expose your children to Chinese culture and artifacts. Part of the purpose of travel is education, and since you are in China, you should at least expose them to glimpses of foreign art and culture.
(I think back of my parents "dragging" me to foreign museums when I was a kid. It might not have been what I wanted to do at the time, but now I recall my first exposures to interesting cultures.)
The Shanghai Museum is the best English-friendly museum in China, and the exhibits are arranged by medium. Thus, there are sections on calligraphy and scrolls, bronze and currencies/coins. More interesting to the kids are ethnic costumes. There are fascinating displays of Chinese porcelain. The gold, jade and gems are also interesting.
Since the Museum is free, I suggest you go early on a weekday and spend an hour at most. If the kids show some interest, you can go back another day. I find the boredom many times is the result of too long a visit rather than the Museum itself. Small doses work much better. Since it is free and centrally located on Peoples Square, why not?
You can really have an interesting time by taking the family into a small noodle shop, or a hot pot restaurant, showing types of food they will not find at home. Fuxing Park is very interesting to watch the adults sing, dance and exercise and let the kids play. Old Shanghai is a neighbohood south of Fuxing Road. There is really nothing "old" about the City God Temple and YuYuan Garden bazaar and complex north of Fuxing Road, the common stop on the tour bus. Frankly, many of the stops on the bus tour are tourist traps plain and simple where natives rarely go.
So take the kids to the real Old Shanghai, to some real Shanghai restaurants (with English translation menus) and on the Metro subway rather than the tour bus. Let them see ordinary Chinese students and workers riding the world's largest and most modern subway system. (Avoid Line 10.) Quite surprisingly, they are just common folk, like you and I.
I would spend a day and a half in Shanghai and then a day in a watertown. If you are not going to Suzhou to see the famous gardens, the best collection in one place in the world, then at least go to YuYuan Gardens at opening time to stroll the excellent garden with the kids before the tour groups arrive and spoil the ambiance.
The distance between attractions is not too far, maybe 10 minutes on the Metro if planned in advance. (See www.exploreshanghai.com) Lines are not a problem if you visit the YuYuan and Museum early in the day.
PS. Definitely do not do "volunteer work" at panda facilities. It is a tourist rip-off shoveling panda poop. Just go to the Chengdu Panda Base if you have time, arriving at 8:30 a.m. in time for morning feedings to watch the many cubs playing and climbing in an open natural habitat. Zoo exhibits in cages and small areas are depressing.
Edited: 9:35 am, January 03, 2012