Desilu Studios was trying to expand a bit in their comedy range and must have blown the budget on this one. I think that was the reason Fair Exchange might have been canceled after only 15 episodes.
The American Walkers, Eddie Foy, Jr. and Audrey Christie and the British Finchs, Victor Maddern and Diana Chesney to do a little people to people relations on their own. Also maybe to exchange each others problems with their teenage daughters, Lynn Loring and Judy Carne. They kept their respective boys at home, Flip Mark and Dennis Waterman, but in the future had the show lasted, who knows where that might have developed.
I think Fair Exchange was only two years ahead of its time. Had this show premiered when the Beatles started gaining international popularity this show might really have taken off. I wonder if that had ever occurred to Lucille Ball.
As it was my guess was that the production costs for shooting in London and Hollywood were too much and the show was canceled before it found an audience. I do remember I liked the episodes I did see and maybe the idea could be revived.
Come to think of it, it was halfway revived with British cousin Cathy visiting the Patty Duke family and the sights you see from Brooklyn Heights.