Does the run score?

[starman]

I am not an ump, I just read the message board a lot. I was hoping someone could set me straight on this play. This happened in my son's game today.

Bases loaded. 1 Out.
Ground ball to Third.
R2 is tagged out by the third baseman.
R1 reaches and tags second base, however, he gets confused and retreats towards first base. This reinstates the force.
The third baseman throws to second to get the third out. However, R3 crosses the plate before second out. Does the run count?

The ump initially counted the run. The the defensive coach talked him out of it. I did not hear the converstation.

I know that the run would not count if it was a straight forwad double play. However, instinctivly I think that since R1 reached second the run should count. I am having trouble finding anything in the MLB rule book to clarify this.