I feel bad but I find my two year old almost unbearable to be around

He doesn’t listen at all. No amount of discipline or redirection works either. I’m a teacher and none of what I know about children or child psychology works with him. He tests me more than any child I’ve ever been around. He gets in these moods where he purposely harasses me, where he thinks it’s fun to throw things at me or the baby. NOTHING stops it other than physically putting him in a room and holding the door closed. He won’t stay in time out, if I try to hold him he just hits me in the face, so I have to put him in his room and hold the door shut because he can easily open doors. It’s absolutely horrible. He bites me randomly. He tries to poke the baby’s eyes and constantly tries to hit him or kick him. He breaks almost all of his toys. He screams at me relentlessly all day for various things. He hurts the dog. Talking to him does nothing because he doesn’t understand what I’m saying. He just stares at me and laughs when I try explaining something to him. He’s just uncontrollable. I’m at my wit’s end. I hate feeling this way about my own child. He is exactly 2 and half years old. People offer so many suggestions, try and get out of the house, burn his energy out outside, offer various activities, I DO ALL OF THAT, but it doesn’t change his abhorrent behavior.