Visit a family member in China

Hi. I would like to visit my daughter who lives in China with her Chinese husband. I only expect to be there for 2 weeks. I would like to travel with my son. I am an American with permanent residence status in Poland. My son has both a Polish and US passport. Should he travel with his American or Polish passport? Is there a family entry permit or do we have to buy separate visas? What if I buy tickets and then have my entry permit declined for some reason? Is there a way to get entry permit before I have tickets if my daughter or her husband fills out some form? Thanks for your help.