I'm sorry, but your child lost all legal rights to their birth family when you adopted them. Legally you are their family now.
You may feel that the information you want directly affects your children's identity but your feeling doesn't outweigh other people's right to privacy.
There's is also the practical issues of how on earth anyone would keep track of all births , deaths and marriages to everyone related to two individuals . And then relay that information to everyone who wanted to know. And how each of these people would be compelled to give this information to SS.
Some men have several kids over a period of years to many women scattered around the country. Some they will have relationships with, others might be ONS. How would it work for you to know about all of them?
And even if you did know, how would it help your child to know that they have, for example , 4 half siblings scattered across the country aged approximately 4-12 years but no one knows their names or anything about them ? Because he met one of them once and paid some money for another for about a year . How exactly will that help your child's identity?
What about birth mum- many women who lose babies to the system eventually sort their lives out and make a fresh start. They are able to parent another child and have no contact with SS. Why do you think you have a right to know that?
And remember of course that any such legal right would have to be reciprocal and they would have to be told details about you.
Yes it would be nice if you were in contact with the birth family and they were willing to tell you about significant events - that's one thing. But to suggest that they be legally obliged to tell SS and SS be legally obliged to tell you is draconian and an infringements of other people's rights.
I think you need to be more realistic about the uncertainty and lack of information that comes with adoption. I also think thay identity is more complex than you suggest and it's not helpful for you and your children to feel this is predicated upon you being given all the information about your children's birth families - past, present and future.