While growing up, I was a faithful subscriber to Sports Illustrated for Kids. One of my favorite parts of the magazine was a section titled, "You Make the Call." There were three situations every issue that tested your knowledge on the rules of various sports.
Here is a Little League situation that I came across today. You make the call:
Runners on first and third, one out. Batter hits a fly ball to centerfield which is caught. Runner on first left when the batter hit the ball and before he could return, is doubled at first. Runner on third crosses plate before out is made at first. Does the run score?
I remember "You Make the Call" from my childhood which was long, long ago, so it's been around a long time.
It has been many years since I did a little umpiring, but I believe I know the answer to this without going to look it up.
The run scores if the runner crosses the plate before the third out is made, unless the third out is a force out. Getting caught off first is not considered a force out, so in your example, the run would score.
I hope the ump got it right.