Expressing the anal glands properly should not hurt the dog. Uncomfortable, sure, but not where she's screaming like someone is killing her. Either your little one is just very sensitive, or the groomer wasn't expressing her properly.
Keep in mind that once your groomer begins to express her anal glands for her, it's usually a good idea to keep it up as part of her regular grooming. Personally, I'd be pissed if a groomer expressed my pups. I don't think it should be done unless absolutely neccessary. Rather, I'd put them on a more appropriate diet to encourage their body to naturally express them.
One last thing, putting a noose around a Yorkie's neck is certainly NOT the end of the world. Period. HOWEVER, I am really suprised that your groomer didn't also put a noose under her abdomen so that what happened, couldn't have happened. Especially w/ it being her first time having her anal glands expressed. Poor girl.
I'm not saying switch groomers, but I would certainly convey your wishes clearly before she grooms your girl again!