I'm baffled by a preschool with "work" and a 20:1 student/teacher ratio. Is there an aide or assistant teacher you didn't mention? Don't you think he could use a smaller class experience and a more nurturing, less academic or structured experience for his first preschool? I think he feels lost - new home, new neighborhood, new schedule, end of summer and losing his sibling to school, new friends/classmates, new teacher. Who can blame him? He doesn't have the vocabulary, so he hits when he's frustrated. He's trying to be heard over 19 other kids?
No, you can't keep going to school with him. But let's re-evaluate the purpose of preschool. It's NOT to learn to write or do numbers or read. It's to learn to separate from Mom & Dad, to function in a group (sitting in a circle for story time, moving to the eating area for snack, lining up to go out to the playground, waiting your turn when doing the day's weather chart (sunny/rainy, cloudy/clear) or sharing and show & tell. That's IT.
So what is the "home schooling" you feel you need to do with him? Yes - at this point it would be a disservice because it accomplishes none of the goals of preschool. He does not need more time with you - he does fine with you. He doesn't act out when you're in the school. What he needs to do is transfer his sense of authority to another adult and be able to function when you are NOT there.
So, if this environment is too chaotic for him, pull him out. If you can find a smaller and more nurturing, non-academic preschool that has an opening, you can consider it. But I'd give him a break right now and think of another program after a month or two..
Meantime, go to shorter term interactive experiences. Don't just keep him home with you. Go to story hour at the library. Join a local children's museum and go to the exhibits but also to the "classes" where a leader sits with the kids and shows them an animal or some fossils or whatever. Let your child practice sitting in a group and listening. Let him play with the other kids. You may find that some of the kids are younger, but that's okay - let him be the "big boy" and the role model for good behavior. You may also find that many 4 year olds are in preschool MWF so their parents are looking for and signing up for activities on T/TH.
Take him to the park to meet other children. Sign him up for swimming at the Y with other kids and a teacher besides you. Join a gym yourself and let him play in the babysitting room with other kids, supervised by another adult. Call your local Newcomers Club and find a play group so he can meet friends and connect with other adults; then schedule some play dates with other parents where you actually leave and he has to connect and work in a group.
Your child does not have to start kindergarten at age 5 if he's not ready emotionally. Keep him out another year, let him do preschool next year at age 5, and go to public school at age 6. That's what I did with my son. It's fine. It has nothing to do with how smart a child is academically - it has to do with emotional maturing and confidence.
I think, if you reevaluate your expectations of a 4 year old, and accept that your 2 children have different personalities and are learning/maturing in a different order from each other, you can figure out a way to expose this little guy to a better environment for him.