How to obtain Chinese visa for HK born without birth certificate?

I am requesting for L type. I immigrated to USA at age of 6 in 1962, my mother held a certificate of Identification for herself and my five siblings. I was naturalized 1 year later. I do not have HK birth certificate. I have the original certificate of identification, my naturalization paper, US Passport and marriage certificate showing change of names.

My husband and daughters are US born citizens and would like to travel to China, I was told I would not be able to join them because of missing birth certificate. There is no way of getting that, my parents are deceased, I have no information of hospital and birth particulars.