I think it's fair too. If she was in the workforce and did something like that she'd be fired. it's a good lesson you're teaching her Fiona.

...If she is actually teaching the lesson...

I don't have teenagers, so feel free to ignore me! lol But honestly, sounds to me like you are upset and angry and personally I don't like the way you said to your friend when the incident happen that it was "her decision to use DSD again or not" and now you are asking her not to outright.
Your trust issues are not your friends issues to be had or carried. You need to address them with DSD. If you are simply preventing her from working for anyone else because you have issues, I think it send the wrong message to DSD - especially if you haven't informed her you have asked your friend not to ask her to babysit until you feel she can be trusted again.


Appears you need to talk to your friend and work out those issues and work on keeping those issues form your DSD's trust issues iykwim.
Must be tough for you at the moment, I hope DSD will come around and help out and you can all relax and settle in a little bit further.