A lot of that sounds like normal 3 yo behavior (not that you should just accept it!).Sassy back talk, not listening is typical. He loses it at home bc he's held it together all day at preschool and he just can't contain it anymore, home is safe. I agree with everyone else that spanking is a mistake. It teaches that people who are bigger than you can hit you. Makes no sense to try to convey to a kid to stop hurting others by hurting him. I imagine you'd begin to see him hitting his little brother if you started with that nonsense.
I think there is still a lot of room for prevention at that age. When he gets home from preschool is he tired and hungry? Has it been stressful to be at school? Is he jealous that little bro is home with you all day and he thinks he's missing out? Are you rushing around, expecting a battle as soon as he comes in and acting defensively? Maybe he needs some quiet time with you. Much of what he's doing is attention-seeking. The truck thing, for ex. And I think once they get going with something like that, it is easier to keep doing it, and if you are getting all exercised about it, all the better for him to keep going. So if you can keep your cool that goes a long way. Rather than telling him what not to do, tell him what to do and help him do it. "Oh here, this is a great road for that truck" and redirect.
If he is screaming and yelling at you, keep your calm and talk calmly to him rather than getting upset (takes a LOT of practice!!). Whispering, as someone else suggested, also can work. He is getting a pay off for these behaviors-a rise out of you, additional attention, whatever. If you remove that payoff he won't want to continue.
If time out isn't working, stop using it.
Another thing that can help is creating a rhythm for the day. If he comes home from preschool then it is time for snack, then a book, then running around outside, or whatever it is that you do, it can help him. If he knows what is going to happen every day, it is predictable, it can really help. If he comes home to chaos, that will not work for him.
Clearly the holding the door thing isn't working. That would make me so stressed, and my daughter so stressed, it would have to exacerbate the situation. I am all for walking away. Calmly tell him "you may not speak to me like that, let me know when you are ready to be kind" or whatever it is then go on about your business. After a few times, he is not getting his pay out, he may change his behavior. Same with hitting."You may not hit" and separate from him. It's no fun for him to continue hitting you if you aren't getting upset and are walking away. Yes, he may follow and continue to try to hit you but if it comes to it, take the little one and go into a room that you can lock yourself into until he can calm himself. It won't work the first time but if this is all he gets every time he does that, he is likely to stop doing that. With DD as soon as she gets over the behavior, we go back to business as usual, there is no arbitrary time of separation or shaming or talking about it or whatever. As soon as she can be polite and calm, business as usual.
I find that often if she is wigging a lot, it is bc I am doing my own thing and she simply needs some time with me. Stopping what I am doing to sit down and read a book can go a long way for her sometimes.
I think talking about control may exacerbate the situation. Yes, clearly he is controlling here, but fighting it out for control can be a looooong battle that results in a bunch of losers. Finding a way to eliminate the controlling behaviors is really what you want. If you are going into it thinking about it being a battle, it will be. A book I found helpful (for all ages) is How to Talk So Kids Will Listen. You may want to check it out.
Another book I liked was Playful Parenting. Sometimes making something into a game can diffuse a situation. DD has said "No" (with great defiance and laying down the gauntlet) to some request and rather than battling it out over the no, changing the dynamic by being goofy or something, has solved the problem.
I think different things work for different kids, and not everything works all the time, so the more tools you have at your disposal the better. I think consistency is so important. If you say x will happen if DS does y. Then x needs to happen. And it needs to be immediate. Good luck. 3 is tough, though 4 they get more willful so getting a handle on it now is definitely a great idea.