I can completely sympathize since, to some degree, my youngest was/is like this. He's a little over 5 now, and has improved significantly in the past year. When he was 3-4 years old, I felt like you do now. His behavior affected everyone in the family.
With my son, a lot of it is sensory stuff. We couldn't afford "real" OT, so we did a lot of Little Gym classes and other physical activity. The weighted blanket was a lifesaver because it helped him sleep. Once he was sleeping better, a lot of the angry and impulsive behavior improved.
One suggestion I have for you that I wish someone had told be about is that you can request an evaluation through your public school district. He may qualify for certain services (including OT, depending on your state/district) through them.
Another thought is to switch up which parent does what. Bedtime was extremely difficult for me, so my husband started taking care of it. I would just go to another part of the house. So, maybe have your husband take care of school drop off?
Tara
living a crazy life with 3 boys
I am thinking now
of grief, and of getting past it;
I feel my boots
trying to leave the ground,
I feel my heart
pumping hard. I want
to think again of dangerous and noble things.
I want to be light and frolicsome.
I want to be improbable beautiful and afraid of nothing,
as though I had wings.
~Mary Oliver