You can also use just a teensy bit of coconut oil (I use 100% organic virgin coconut oil), rub it all over your hands and 'massage' the mats. The oil will 'vanish' into her hair and skin...and yours...and make the hair slippery enough that you can pull small bits of hair out of the mat with your fingers, the end tooth of a wide tooth comb or a 'rat tail' etc. until it is not tangled any more. Plus, if she licks the oil, it is good for her, too. "Montana" brand (maybe "Montana Land" but "Montana" is in the brand name and that's the one you want) Emu Oil will work, too...always use TINY amounts...you just don't need much since teeny tiny bits go such a long way with emu and/or coconut oil. They LOVE the emu oil, too.
I am so glad for you that the first groomer put your hackles up enough for you to walk away. If she had not reacted the way she did, you might have left your baby only to come back to get her and find her shaved down to the skin. I'd say, "bullet dodged!"
She is adorable...good luck.