Is thinking about hitting children—without actually doing it—natural, and what does it represent when images of harming children come to mind, and is this a cause for concern that the mother might harm her children?

These are baseless delusions and should be disregarded. Instead, one should occupy oneself with the morning and evening remembrances (adhkar), reading beneficial books such as works on the Prophet's biography (seerah) and the biographies of the righteous, and attending lessons of knowledge. As for children, there is no harm in disciplining them with a light, non-bruising tap if they do something that warrants discipline. However, if there is no reason for discipline, then it is not permissible to hit them.