scoring a run and the third out - tagged versus force at base

Question
Situation:

Two outs, man on first and third.  Ground ball is hit to the second baseman.  He fumbles around with ball, there is a delay in him tagging the runner advancing to second base, prior to the runner reaching second base.  In the meantime, the runner from third scores.  The other team was arguing that the run should score because in order for the run not to count, the runner from first to second would have had to have been forced out at second base rather than tagged.  

Should the run have counted even though the runner from third scored prior to the runner to second was tagged?

Answer
The thing to remember about force plays is that they are dictated by the situation, not the act of a player.  In other words, the guy on first was forced to advance to second the moment the batter hit the ball.  He will continue to be forced to advance to second until either he touches second or the batter is put out at first.  With that being said, all force out rules apply to the runner regardless of any play made on him.  So although the out was made by a tag, he was still in a force situation meaning the run would NOT count.  I hope this answers your question.  Feel free to leave feedback :)