I've been trying to find evidence from anyone other than Emma herself on the Cox sisters' supposed vulgarity, but haven't come up with anything (from the omniscient narrator, from other characters...).

Is this idea that that the Cox girls are "vulgar" another one of Emma's fancies? Are they, like her conjectures about Jane Fairfax's adulterous inclinations, equally free of empirical evidence? Because if Emma is basing her opinion solely on their father's class/status (i.e. he is a "half-gentleman", ergo they are "vulgar"), then it shows how inconsistent she is, because she can consider a former governess like Mrs Weston or a future one like Jane Fairfax as models of ladylike behavior or elegance -- which, of course, they can be.