Grover Cleveland and Theodore Roosevelt certainly had young children while they were in office. I doubt that the list on the site you linked to was meant to be exhaustive.
Depends upon what you consider a child? Does Margaret Truman count?
Theodore Roosevelt had three or four kids living with him when he was president also.
Tyler had a bunch of kids (in double digits) from his two marriages and I imagine that some of them might have lived in the White House, although he was a widower for most of his term. He met his second wife in the aftermath of an explosion of a steamship that killed his secretary of state among many others.
Franklin Pierce’s sole living child died en route to Washington DC before the inauguration. It was a train accident.
By my count, all the presidents together had 146 children (not counting Geo. W. Bush’s kids). At least a few of them died before their fathers made it to the White House, and many were certainly already on their own. In addition, there probably were some young children who were sent to live with relatives or at boarding schools, so they could grow up under more normal circumstances than the White House can provide.