As I have pointed out before you DO NOT have to provide a BC of your children to get a divorce.
That is not correct.
The issue of requirement for a birth certificate in a divorce proceeding involving children; particularly children where the parties are purported to be both parents; and particularly when the children are under twelve or fourteen; depends on the local jurisdiction; and further depends on when the issue came up.
In the modern world, most of this stuff is now handled by a separate court division, Family Court; which usually, in most jurisdictions has it own local rules. And in the modern world, generally, for the child of the parties under twelve, the most common rule would require a birth certificate.
In 1964, seldom were there Family Courts; most local rules didn't address family law specifics. The local judge or judges would have decided on a basic pattern which would have been communicated the lawyers who did divorce work in their courts--actually, would be surprising to me to find, even in 64, a judge who didn't make the parties produce a birth certificate at a minimum. And I suppose I wouldn't be surprised to find that the judge didn't force the parties to prove the identity of the child at issue to the birth certificate. Matter of fact, I doubt today a court would do that.
So what you are saying is you really don't know.
I know what happened in the cases I am familiar with. Divorce in WA in 1959 (my mothers) no birth certificates since she didn't have them for us kids. Divorces in CA in 78 and 83. More Divorces in WA in the 90's. In none of these were childrens birth certificates required.
In the divorce packets they go STEP BY STEP, telling you exactly what papers to fill out and what papers to bring for filing. Never are you asked to bring a copy (certified or otherwise) of Childrens BC to have put on file.
The point I am making is don't get hung up on the fact that there APPEARED to be a missing paper (some think BC) in Stanley Ann Dunhams (supposedly) divorce papers. Besides how do we know that, that, divorce paper is even real. It has been proven that date stamps have been forged on other legal documents surrounding Obama.