I don't understand why your psychiatrist keeps trying to stabilize your difficult child's ADHD when your difficult child has a mood problem. I think, if memory serves me right, you've had this problem for a long time.
It doesn't matter what your child's diagnosis "technically" is, in my opinion, your difficult child has a mood disorder. THAT, before anything else, should be tamed.
I found this site ~ if you have the time and patience to read through it, it may give you some light:
ADHD is almost always co-morbid with Bipolar. My son, Dylan, is ADHD with the BiPolar (BP). But you know what? The ADHD can't be treated. He cannot handle stimulants. Ever. With that being said, I'd rather have a stable Bipolar child that is in a more structured classroom and gets extra help with school work, over an unstable Bipolar child that might be able to pay attention now and then. I think you are going to have to weigh what, exactly, you want to "fix" the most, and take it from there. If it's Bipolar (or Cyclothmic, whichever) symptoms, you're not going to be able to use a stimulant.
I have a child that is BiPolar (BP) and I have a child that is ADHD, Combined Type. There is an enormous difference in J's lack of focus/inattentive/hyperactive behaviors compared to Dylan's hypomania. J needs to be redirected alot, yes, and is hyper, yes, but on the Concerta, that all is tamed within 20 minutes. When the medication wears off, he goes back to being inattentive and hyperactive, but he is not angry or aggressive. He does not talk wildly or at such a fast pace that what he says makes no sense as Dylan does when he's manic. J can sit still, even without medications, where when Dylan is manic, he cannot. He cannot fall asleep, he cannot function properly, and everything and anything triggers problems. My Bipolar son is NOTHING like my ADHD son, and for sure, if I, a big nobody but a mom, can see differences, your psychiatrist should definately be able to as well.