New step grand parent

They're just dating.
No need for anyone other than his parent to be handling anything, surely?

Ok, Bradford has a point. You haven't told us, Nana70, if the boy's mum is dead, if he has been out of her custody, or if divorce has simply disrupted the life he was used to. Any of these could cause him to act out this way. Perhaps you and dh would do well to be a little empathetic towards him. DD, too, of course, but, imo, she needs to think about whether or not she's prepared to deal with this problem if the relationship becomes permanent.

Still, if his dad can't seem to handle him, I don't see how anyone can expect others to. And as long as you and dh don't have the boy on your own, I don't see why you would be expected to control his behavior, anyhow. That would still be up to dad and he might resent anyone else stepping in. Dad and child may need to get into family therapy if they aren't already. But, of course, that's not your call.

Bradford, in a general way, I get your saying any adult who interacts with this boy needs to "give him room to grieve," but what does that mean in specifics? Are you saying, Nana and dh have to accept his acting out in their home? I don't see that. Imo, they need to be understanding, but the poor behavior still has to be stopped, especially with gd around. And stopping it, imo, is still up to the dad.

Don't forget boys are naturally a lot more physical than girls!

It does sound as if the little boy needs some TLC and structure in his life. If this a going to be a serious relationship then you need to sit down with both parents and talk frankly about child care and all of your expectations. It's difficult I can understand when your daughter and granddaughter live with you.

I'd guess the little boy is wild and destructive because he's lost his Mummy (or doesn't have the same family structure he used to have ) but hasn't the vocabulary to tell anyone how he feels.
Infinite patience, love and time is the only key to this very common behaviour.
It's not going to go down too well either that he now has a three year old 'sister' to contend with. They are both going to need lots of hugs and understanding.

I don't agree it's just up to Dad, it is up to anyone who spends time with this little lad to give him room to grieve and learn that he is still loved.

Where is the little boy's biological mum in all this?

You don't have to handle the boy at all, that's up to his dad and maybe your dd if he gives her that authority. Like Esspee, I imagine that you still get a chance for one on one time with gd if she and dd are still living with you and this man and his son are not. If they move in together, that may be a different story. But that might not even happen.

How long has she been dating this man? Do you think it's a lasting relationship? How does she feel about his son's behavior and the possible influence on gd? Any chance that she'll think these things over before making this relationship more permanent? I know the boy is only 3, but if I were dd, I would hold off on getting too involved or moving in until I saw if his behavior gets better or not over time.

Regarding 1 on 1 time, unless the boyfriend and son have moved in surely you see a lot of her? You can offer to babysit your granddaughter. The boyfriend should arrange his own babysitter. Just be firm.

Had the boyfriend moved in to your house?
There is no obligation for you to have the boy in your home if his behaviour is disruptive and no obligation for you to babysit. Simply state that you can't cope with his wild behaviour.