Child-friendly accommodation suited to family holidays or breaks in Beijing includes the Sandalwood Marriott Executive Apartments, with a kids' playroom and a pool; and the extraordinary, uber-luxurious Commune by the Great Wall, with interconnecting rooms, some with Wall views, several contemporary houses dotted amidst its grounds (one with its own tea-room), and a kids' club for ages 3–12, with activities including Wall outings.
There's also a plush Peninsula hotel in both Beijing and Shanghai, with the Beijing incarnation offering Kids' Academy activities for ages 6–12, including the likes of kite-making and candied-apple making. In Shanghai, you can might try the cheaper Bund Hotel, with rooms with two double beds.
Hotels in big cities offer child-friendly services such as baby-sitting but the degree of English spoken is usually, at best, minimal.
Prices can be equivalent to European and American prices in the cities, but in rural areas you should be able to find reasonable places to stay for £5–10 per night.
Consider breaking your family in gently by booking an adventure trip (see Trips tab).