Error Scoring Question

[jeschmit]

My mom is the head softball coach at the local high school, and she sent me this the email the other day. It is whether or not the run should be scored as earned or unearned. If anyone could help me out with giving her an answer back I would greatly appreciate it.

I have a question about an error.
In our game on Friday. Taylor was pitching - in the inning they scored their lone run -- this is what happened. My question is, should there be an error and/or earned or unearned run. We ended up winning the game, but the scoring was as an error on the 3rd baseman and an unearned run -- not sure I agree since the runner didn't advance.

Batter 1 on the inning -- Strike out (1 out)
Batter 2 on the inning -- walk (1 out, 1 on first)
Batter 3 on the inning -- base hit - advances runner to 2nd (1 out, 2 runners on --1st and 2nd)
Batter 4 on the inning -- walk (1 out, bases loaded)
Batter 5 on the inning -- Fly ball to SS - caught and then tried to double-up the runner on 3rd - first looked to 2nd base and then we were al yelling 3rd and she threw to 3rd and 3rd basemen dropped the ball - however no one advanced. Error?? If so - who? (2 outs, bases still loaded)
Batter 6 in the inning -- walk (run scores on the advancement of the walk - still 2 outs, bases loaded)
Batter 7 in the inning -- Strike out (3 outs)

Can you assume a double play and can you give an unearned run after a mis-hap double play that the runner didn't advance on??
Please shed what light you can on this. Obviously it is a big decision as far as the earned run and giving a player an error.
I appreciate your insight.

This is the email she sent me, so this is written in her words, not mine. So if anything is confusing, I'll have to ask her.