Bad situation.

[Rachel]

The coach must have played college softball. You must pull the bat back in the NCAA. You could have informed her of this quietly when she questioned you.

Fair foul is not determined by the batters box. Call the coach over and calmly explain this. Use your "Verbal Judo" to discuss and descalate the issue. That book by the way is a must read for an umpire.

Just because you call a low one early that doesn't mean you set the strike zone there. Try to call the correct zone.

Don't talk to the fans.

if you feel the coach is deliberatly riling up the fans warn her to stop and then eject.

The poor sportsmanship of the coach after the game could be addressed with an e-mail to the AD. I don't know your situation but in my state we are beginning to have the officials rate the schools in sportsmanship.