Both Vernon and Percy then signed up for duty aboard the Lusitania - the giant unarmed British liner sunk by a German submarine off the coast of southern Ireland on May 1, 1915 with the loss of 1,195 lives.
The tragedy hastened, if not precipitated, America's entry into the war.
Both men survived despite Percy initially being reported missing. He was drawn down into the water by the Lusitania's vortex before being blown to the surface by the counterforce of her exploding boilers.
Julia and Ethel received simultaneous news that both men were safe - resulting in a joyous reunion on a Liverpool tram.
Vernon and Julia's daughter, Catherine, carried one of her parents' two Carpathia Medals on her key ring for many years, explaining its worn condition.
Auctioneer James Morton said yesterday: "The sale of the medals reveals a remarkable and poignant tale of love, courage and survival amid the horrors of war and the terrible loss of life on both the Titanic and Lusitania."
Included with the medals, being offered by the family, were a Carpathia dinner menu; a signed photo-card of Carpathia's Captain Arthur Rostron; a picture of seven of the ship's stewardesses, including Julia; photos of Julia and Vernon in an off-duty moment on the ship; and a 1915 telegram from Vernon's brother Laurie (whose war medals are also being sold) bearing the words: "Thank God for safety."