How fortunate you found that scrap of paper in Izaak's court naturalization records.
Assuming all three children were later issued Certificates of Derivative Citizenship, they would all have C-Files containing records not available in court records (so not available at the National Archives).
Unfortunately, the number on the paper is the application number, not the C-file number, so you would still need to file a USCIS Genealogy index search request to obtain the C-File number, then request the C-File. The number will be preceded by a letter "A" or "AA."
Derivative C-Files are usually full of information, extra photos, and certified records submitted as evidence (birth records, parents' marriage records, etc.).