http://iscoresports.com/

If there is a runner on third with 2 outs and the runner on second or third is put out for the third out with a force out on a fielder's choice, I have been scoring it when iscore asks what happens to runner on third as runner was safe at home but run not scored. I noticed the official scorer for my daughter's college team's games scores it as runner remained on third.

Which way is correct and does it make a difference in runners left on base at the end of the inning either by how it should be or how iscore records it?

Makes no difference. If bases are loaded, you have to move the runner to home (and use run not scored), as there is no place to put that runner.