Hello and welcome from me! Thought I'd go ahead and throw my thoughts into the ring, too.
This is just my personal opinion, but I do believe that Millie's list of classic Cushing's symptoms, the calcinosis cutis, and the positive LDDS all "trump" the ACTH and point to a genuine Cushing's diagnosis. Even though the ACTH is less prone to "false positives" than is the LDDS, it is far more prone to "false negatives," especially for dogs having the adrenal form of the disease. So in a situation such as this, where Millie is so symptomatic but has turned up with a negative on the ACTH, the recommended protocol would indeed be to turn to the LDDS for further confirmation. The abundance of false negatives on the ACTH is probably the main reason why many specialists discount the ACTH as the initial Cushing's testing tool, although I do believe there are situations where the ACTH has a testing advantage (but I won't bore you with an explanation here).
On their own, Millie's LDDS results do not distinguish between the pituitary and adrenal forms of the disease. But her ultrasound is consistent with PDH since both adrenals were enlarged. So if it were me, I would feel as though your vets are making the right decision in pushing ahead with treatment given Millie's entire symptom and testing profile.
One quick question for you: you mention that she is also taking phenobarb. Does she have a seizure disorder? I will come back and add another reply about the phenobarb, but it may end up having an effect on the trilostane dosing down the road.
Marianne