The fastest and easiest way to request your father's records is to use the eVetRecs portal. Click this URL and follow its instructions. eVetRecs Help | National Archives
Be sure not to submit multiple requests since that will push your inquiry to the back of the queue.
That will give you his personal military history from records we have in St. Louis. If you'd like to know what his unit (if you know it) was doing, you would need to come to (or hire someone to come to) the National Archives in College Park, MD. You can send an inquiry through this online form ( Contact the National Archives | National Archives ) to verify that NARA has his unit records before you make the trip. A response may take a month or more so be patient. One tip is to also ask if there are any photographs of his unit.
As far as his children are concerned: The National Contact Center, part of the General Services Administration, may be of help you. The Center has links to military locators and information about finding private individuals from the Social Security Administration, the Internal Revenue Service, the Department of State, and the Salvation Army.
National Contact Center (GSA)
Books and articles on locating private individuals:
Hinckley, Kathleen W.
"Locating the living: Twentieth Century Research Methodology."
National Genealogical Society Quarterly, 77 (September 1989): 186 -196.
Martin, Amy Suzanne.
"Playing Detective: How Government Records and the Freedom of Information Act Can Help You Locate a Missing Person."
Heritage Quest 7 (July-August 1991): 7-8.