Z Visa and Family Members

Hi, My family moved to Guangxi where I accepted a position at an IT firm. We came over on L types and I'm now applying for a Z type. We were unclear on how my family would receive long-term ones once I get me Z type. My personal invitation says Hong Kong, so I'm planning on going to Hong Kong in a couple weeks with all of my docs to obtain it. The problem is that my family's document authentications are currently in process in the United States. Do I need to wait for those docs to be in hand with me in China before I go to Hong Kong, or is it enough for the appropriate offices in the in US to approve of our marriage certificate and our children's birth certificates?

Thanks!