Does the run count

Question
Bases loaded one out.  Catcher catches pop up for 2nd out.   Runner on third
holds on third, runner on 2nd holds on second, but runner on 1st takes off
before tagging up.  Catcher see runner from 1st heading towards 2nd and
throws ball towards 2nd (this is 10U girls softball) but over throws into center
field.  Runner from 1st was heading back to first, but when tech coach see the
ball has been thrown into center field turns she sends her back to second still
without tagging up.  Center fielder throws ball into 2nd baseman who tags
the girl from first out...3rd out.  Now the runner from third crossed the plate
before the tag was made...I say the run counts.  Am I correct?  Also, what if
the girl was not tagged, but the ball was thrown to 1st before she made it
back?   Does this constitute a force out thus negating the run no matter when
it crossed the plate?

thanks.  

Answer
Boy, Mark, you really have me scratching my head on this one.  I think that since this was an apparent in-field fly rule if fair then the runners are running at jeopardy.  If this is the case, I would score the runner either way provided she crosses home before the third out is made.