My daughter is SWCAH now age 11 yrs.  She went to a private preschool. Both her dad and I worked full time.  In our case we just made absolutely sure that we gave specific instructions to the entire staff on how to give the shot.  We gave them a print out ( I like the one from the Texas newborn screening site) that tells all about CAH.  What it is, why it is and what to do.  We basically told the teachers and director (and in our case they all knew us from the church so they were probably more willing than other places may have been) that they either had a choice to stand there and watch her go into crisis from whatever was wrong with her or something even worse or learn how and administer the shot.  They all agreed and practiced on oranges.  Turns out she did bust her head open at school and needed a shot.  They had called me, called the ambulance and was getting ready to give her the shot but I arrived within 5-6minutes from work so I gave it.  The ambulance drivers did tell me they would not have but would have encouraged the school to give it had I not arrived when I did. 

Honestly, she probably could have waited to get that shot.  We were new at it back then and panic sets in quick.  In all reality unless they are already in a crisis situation that shot can wait a few minutes.  She was bleeding and crying and obviously upset from all the commotion but she wasnt in crisis yet.

As she got older and went on to a public school they had a nurse onsite and we gave her the same info and oranges practice.  She hadnt had to give a child in school a shot but was willing.  Two years later we moved and that school also had a nurse but she was not as willing.  I had to go to the school board.   We had to write a letter and it was on record what we wanted done and how.  They just wanted to cover their butts. We didnt blame them.  Turns out we moved again and this school that she is at now is a private one and I work at the library there.  Convenience.  Good luck. And yes push the issue.