The right groomer will help peppa overcome her fears, she may not ever enjoy it but hopefully will learn that nothing bad will happen while she is there.
My girl is not a fan, she has a good old moan and groan when the dryer is on but her groomer (who has years of experience) has worked out that Bea likes to have Ollie her jack Russell in with her, there are no other dogs there as she only works on a one to one basis.
The result is a little less moaning etc

Sounds like you have some recommendations for your area already, I'm sure she will be fine.