Naughty behaviour in 3year old

That was a typo
I am not that bad at maths

5.40 am is really 6.30 am - he won't know about the clocks going back.

I expect the routine at his dads may be different than at home. bed times may be much later, discipline may be lax..
I've lost count of the number I've times I've heard mums say "he/she is always like this when he/she comes back from their dad".

The Thunderous Threes
Often worse than the Terrible Twos

You have to be firm, consistent and let him know he is still loved by everyone.

Maybe your daughter needs to talk to the child's father and see how things are when he stays there. They need to be consistent and firm when dealing with this behaviour. The little boy is insecure and worried about the family separation, if the parents work together they can reduce his anxiety. You can help Greciangirl with love and support. Toddlers can be a nightmare all on their own without adding a family split to the mix.

My lovely DIL has always said that the terrible threes were worse that the terrible twos....

How is his behaviour at nursery?

its probably his parents split thats the root of this.My GD had a really awful few months after her parents split ,she was moody and refused to do anything that was asked of her .She settled down eventually until Daddy announced he was getting married and then we had a real meltdown,she didn't want her dads partner ,who she got on well with,to have the same surname as her dad and her as it was THEIR name and mummies ,she broke her wee heart on the wedding day and her Grandpa and I had to go rescue her and bring her home with us.People underestimate the result of a breakup on small children and I would give your GS all the love and support you can ,he has no idea why his world has changed and he doesn't like it .

I would check what his behaviour is like at his dad's and at nursery. Is nursery a new thing in his life? He sounds like he's upset about something but is unable to articulate it so is acting out. Look for changes that he may be reacting to, but don't make a big issue of his behaviour. I found with my dd and others I've had dealings with that firm but calm correction usually works best

It sound like the terrible twos, but a year later. Small children do go through phases like this, but I would not discount the possibility of having to split his life between his parents as a contributory factor.