His moods will fluctuate even if he's not BiPolar (BP). We all do. Irritability is a common symptom in both sides of BiPolar (BP). If not following directions like that is a common problem then start putting labels on things or notes on the wall. Easier to say that he should look at the note before doing anything than to argue about what he did wrong.
medications may be your only real option. As you say, it has gotten worse which happens as they near puberty. Unfortunately, it can get worse for awhile in puberty. So early treatment is your best hope of containing it.
I find it helps to think of these symptoms like irritability as a symptom of an illness. If my child is scratching because his skin itches, he's screaming in pain because his head hurts, etc, etc I wouldn't react the way I do to behaviors. So I find it helpful to try to keep the context. The irritability is a symptom.
As to your easy child, you may have to explain to her that difficult child is ill. The rules and consequences for him are different because of this illness. She can't compare how you raise her to how you raise him. This has honestly worked for me. So lots of praise and rewards to easy child when difficult child isn't looking.
