You have every right to be protective of your baby. I worked for a groomer for a while. We never went and took animals out of an owners hand unless that owner handed their animal to us first. Normally, we would let the owners walk their dog over to us. It would normally make the dog feel a little bit better when he could walk and can "sniff" around. We also never gave any personal advice to the owner unelss they asked a specific question! How dare she try to tell you how to reaise your baby!
If someone asked for a specific groomer to pretty their dog up, that groomer would do the job! Unless they were overloaded, but we would tell the owner "So and so has x# of dogs today, is there anyone else you would like, or would you like to set an appointment for them tomorrow?" or "She is swammped today, but so and so does (breed) very well!"
In the shop I worked in there were some very talented and kind ladies. But I also saw alot of bad things happen. Some people are just not cut out to be groomers. Not all dogs enjoy being worked on by a stranger and they squirm, bite, pee themselves, try to jump, etc. and some people don't really know how to properly respond to that. So if you feel uncomfortable about a shop DO NOT hesitate to find a new groomer. If your baby appears to be more shaken up than happy to see you after a grooming you should enquire what has happened and consider moving. Normally yolu can find reviews on a groomer online