You've posted on Derry/Londonderry board so do you think this is where your family came from? It's not near Caledon where your father was stationed in WWII but be could have traveled a distance to go see the relatives. Since the three Mullin children left Ireland about 100 years before that it sounds as thought family contact continued in some form for many years so there might be clues amongst your family in U.S. about a location/people in Ireland.
Where did the 3 children go to in America? each U.S. state keeps its own vital records (births, marriages, deaths) and usually those certficates ask for details such as parents' names, date and place of birth, etc.
Newspaper obituaries often give a place of origin for those born in Ireland.
Any old letters or an old address book of your father's that might give a 'recent' name and address for the people he met here?