Your post reminds me of my friend's grandson. He was diagnosed with ODD (Oppositional Defiant Disorder) at seven years of age. He was removed from the public school system and taxied to an alternative school for about one year. Later, he was diagnosed with severe social anxiety and not ODD.
I am wondering if the ADHD diagnosis is incorrect. It is not uncommon for children suffering from anxiety to be mis-diagnosed. Our own child was diagnosed with severe social phobia, depression and later thought to also suffer from ADHD. The ADHD was an incorrect diagnosis - anxiety often mimics this disorder. If the ADHD medication does not work, this could mean that the diagnosis is wrong. Tantrums and frustration and anger are common behaviours of several of the anxiety disorders. Separation issues and depression are also common to several of the anxiety disorders.
I might suggest you seek out a medical person with experience in anxiety disorders or perhaps a child neurologist or child psychiatrist/psychologist. Even if anxiety is not the correct diagnosis, it appears that the diagnosis you have been given is not correct. I might also suggest you google "childhood anxiety disorders" or some other similar word grouping to see if any of the descriptions match your son. I wish you the best -
ADHD is actually extremely rare and one of the most overdiagnosed and poorly defined disorders. I would read up on it and see if it could be controlled more readily by diet.