Can a tourist visa be extended? Can a person leave China and re-enter holding a 30-day tourist visa?

We--my two sons and I, all USA citizens (and my sons have Japanese passports as well)--are in the process of moving from Shanghai to Beijing, where I will be starting a new job. At present we have tourist visas good for 30 days, but I am going to Hong Kong tomorrow to get a 3-month or 6-month visa (since I am told by my new firm in BJ that the 30-day visa will not allow adequate time to get a work permit and residence visa. But now what about my sons? Can their 30-day visas be extended once we are in Beijing? Will they need to leave the country? (And will I need to leave the country again?) If one or both of the boys do leave the country (to go to Japan), can they re-enter with the current visa, issued in Shanghai, or do they have to apply for new visas or do something else? A lot of questions! If it is possible to talk by phone that would be great! Thanks, John