Don't be scared.
It is just hair. It will grow back. Believe me...
Dogs are wiggly. I'm fairly tolerant about mine getting hurt by somebody if they tell me what happened (in the case of wuicking a nail, I don't care at all). She should have showed ou so that you could watch it. I would not trust her.
I'm not into dropping the kids off and leaving them with random people either. That'd be a big no for me, esp. if I barely knew the groomer. My dogs are not show dogs, so it doesn't really matter. I can't justify paying for somebody to whack off hair when I can do it myself (but that's me).
I'd skip the dremmel and get nail clippers. Everybody quicks nails. No big thing.
(btw, I don't fix my hair and paint my nails about twice a year max - not my thing)