I think you are probably mistaken. As far as I know it is one passport per application. As a kid I was on one of my parents passports. Since the 1968 Dunham application is a renewal, it is not clear if Barack was on her passport or not. I guess we would have to find a 1965 passport application to see how it was worded.
It seems to me that Barack Jr. probably had a separate passport from his mother. Otherwise, she would have had to file for an amended passport to remove him when she wanted to travel alone. Of course it is possible that that is one of the missing applications.
No, there was no separate paperwork done for me as I was on her passport application. I had my own separate passport but my mother signed my passport with my name and stating that "The mother signed the passport."