I agree with the above regarding consistency. Consistency is required. Children need to know what to expect. It helps them to feel safe and secure. Be prepared for his behaviour to escalate as he tries ever harder to get his way. When he realises that he won't get his way his behaviour will de-escalate. However, if there is even one moment of inconsistency, his behaviour will escalate again and will take even longer to de-escalate this time as he will believe that he will get his way eventually.
If you are not sure why the behaviour is occurring only at home then I suggest taking notes. For instance, fill in an ABC chart. Column A= antecedent (what happened before behaviour, such as saying 'no' to a request for lollies). Column B= behaviour (what behaviour did you observe, such as kicking). Column C= consequence (what happened afterwards, such as punishment for the kicking). This will help you identify what triggers the behaviour. Also note down what time it happens and how long the behaviour occurs for. Do this for 1 week then see if you can identify patterns, for instance, it almost always happens after you have said no and your son knows he can get his way anyway. Once you identify any patterns, you put in place a plan. For instance, when you see 'good' behaviour (quietly reading etc) without it being a battle for him to be engaging in that behaviour, praise him. Provide him with positive reinforcement (your attention) whenever he is doing something well. You could pair your attention with a small treat and then gradually phase that out but that might be problematic.
Does he get enough attention at home or does he engage in this behaviour because he doesn't get enough? Maybe he is exhausted after child care? Lack of sleep can cause children to be unable to sleep. Conversely, maybe he doesn't need to nap during the day and he is not tired at night. If he is not tired, perhaps you can set up quiet reading, drawing etc in his bedroom with a dim light at night. He can (hopefully) get himself to bed when he is tired without engaging in aggression etc.
Do you provide options? Such as him choosing which pyjamas he wears, when he brushes his teeth (before bath or afterwards), which bowl/cup he would like to use etc. These options are not problematic for you but would provide him with a sense of control. Could he be entrusted as a helper? Eg. helping with dinner preparation (washing the vegies, cracking an egg, stirring etc). I know Montessori education centres promote independence in children so perhaps he feels independent whilst in care but when he gets home he feels he is not trusted.
Does he have any winding down/relaxation time before bed? Eg. TV off, other devices off, quiet activity time (reading, drawing, cuddling with mum or dad etc).
As a side note: whining is actually seen as a sign of intelligence in children.
Hope this helps!