Is he half yorkie and half poodle? I'm not sure if poodles have undercoats or not....I googled it and find mixed info. Does Charlie shed?
I would go to another groomer and ask about the undercoat. Have them show and explain it. I know that my Maggie does not have an undercoat. All of her hair is the same color and soft (not wiry) texture and grows at the same speed. She does not shed a bit. When I haven't combed her in a while and then comb her I will pull out a very small amount of fluffy hair that reminds me of a dust bunny. I think she has yorkie hair and not poodle hair. Yours might be poodle haired.
When I was little my mom made them thin MY hair. I hated it! They used a special pair of scissors that looked like that had sections missing. (here is one)
Classic Products Diamond Line 30 Tooth Thinning Dog Shears
They cut in the hair, closer to the root and cut out some of it, while retaining the length.