Without answers to my questions, I can only make suggestions.
If you have had a life change of any kind at home or school, like a new daycare worker, or someone leaving daycare, a new person in the home, death in the family or illness.. someone is busier at work, then this is likely temporary until he adjustments. If he has been home sick or had a holiday, that can also stir things up. I'll assume he's had a physical lately and has seen a dentist and that you know he is well and not in pain.
At three he has some understanding of consequences and the behaviours you expect and that are expected at daycare. I worked in the classroom next door to a daycare in my school and though they certainly had children with behavioural difficulties -- including serious ones like those earning an 'autism spectrum' diagnosis, they never refused care to any child or family unless the parents were abusive to staff or did not pay their fees. So though the daycare might let you think your child is at risk, it is not likely unless they are not licensed. (I can only speak to North American practice.) They should have experience with naughty children and perhaps they've already made suggestions and you disagree with them. Try cooperating and coming up with a plan for both places -- that is the best possible solution.
At home, if you cannot take a day to shake things up, try sitting calmly and explaining why this is serious. He understands more than most would give him credit for, and he might have a very good reason for acting out. That is the root. You must be completely honest with him and tell him that you will be taking very serious and not very nice measures until he listens. Do not exaggerate. Do not lie. Make sure everyone is doing the same thing because consistency at home is critical to it working. Do not threaten. If you said that the next time he does 'x' you will do 'y' -- then you must do as you say. An idle threat is just a way to say "Keep fighting and we'll give into you."
If this is as serious as you say and he cannot or will not give you a reason and your usual token systems are not working, then you either see a professional or you take everything away and slow re-instate things as he earns them. This is a serious commitment on your part and on the part of other family members and I would not do it unless all other paths have been tried.
You could start off with just removing TV for a 'week' and see if that works. It is impossible for me to say how serious a problem you are having.
If it is really serious behaviour:
You empty his room of everything breakable and all breakable toys. He stays in there if he comes home having had a bad day at school and comes out for a meal. If he cooperates and obeys at mealtime, he stays out of his room -- but there is no TV/computer/tablets for anyone in a common area until this is 'fixed'. (You may well have to remove them from the area -- or at least remotes and so on.) It has to be unplugged. That TV etc. will take him that set number of days to earn with good behaviour at school and at home. You or the other parent may find that you have to stay in his room to keep him there.
Everyday he is good, something is replaced (you have to give him opportunities to prove that he understands and wants to do better) -- but not the big stuff until the set number of days have past.
In the future, if the above or any part of it has worked, then I'd also implement the following:
- Reduce the amount of noise at home. By 'noise', I mean too many toys, clutter and TV, music and shouting all happening at once. (I know this is normal, but reducing it reduces stress.)
- Never lie or threaten. Never pick a battle you won't see to the very end. If you need to sleep -- do not threaten something that will keep you up later. So be aware of what you say and what you do.
- Make punishments fit the 'crime'. If he breaks a toy -- do not replace it. If he breaks a sibling's toy -- he loses his favourite toy -- permanently.
- Make praise real. Notice when your children are being good. Show interest in their activities. Take the time to talk about worries and triumphs. Do not accept "Good" as the answer to how school was. Learn to ask questions that require a more detailed answer. Be generous with real praise. Asking your child's opinion works as well as praise.
- Be as generous with your time as is possible. Include your children in your chores -- even if they are just sitting in the kitchen while you prepare dinner or fold laundry. Let them help if it works for you but do talk to them about what you are doing and why and how you do it.
- Make sure that you are allowing your children to make as many choices as possible. Choices make children feel like they are a part of what is going on. You give them two or more choices from selections you have already made and that are agreeable to you. Red/blue shirt. Corn/carrots. Applesauce/banana. Blocks/stuffed animals.
Thoughtful parenting will make your life easier, but it is a huge time and effort commitment. Of course you are tired after a day at work, but your kids honestly don't see it that way. They have also had a full day away.
