I'd try writing her a letter or email, tell her that you've no intention of spending Christmas, or any other time with them socially, until she has taught her child how to behave. Tell her all the things that you're unhappy with, and point out that it's her job to teach him, not down to him to miraculously become well behaved, when she's not putting any boundaries in place to help him. I would also point out that he's going to school soon, and ask her if she really wants her child to be the one that all the other kids avoid because he's not been taught how to share, make friends, or whatever the problems are. You could, if your parents agree, even tell her that your parents don't enjoy having them there, because while they love him to bits, he breaks things that they've worked hard for, and that upsets them, and is even causing problems between them. I would also mention that your children don't want him at yours because he breaks their things too. Tell her that this in NOT acceptable behaviour for a 4 year old, and her excuses about him only being little, no longer wash. Then sign off by saying that you love her and her child, and feel that as her sister you need to tell her the truth, before someone else does. You could perhaps offer to help her with some ideas of how she might get through to him, or maybe suggest a parenting class in the area. Obviously word your letter to suit the things that are happening, I've just tried to give you some ideas.
The thing with writing a letter or email, is that the recipient is forced to read it, and can't argue or interrupt what you are trying to tell them, so you have a better chance of getting your point across.
She will likely call you and react angrily, or she might call your Mum expecting her to agree that you're a nasty interfering bitch, or whatever, so it might be worth warning your parents what you plan to do, and suggesting that if she does call them, that it's their one and only opportunity to join forces with you, and tell her that you're right, and that she does need to get a grip on his behaviour. It sounds like your DF would happily back you up, but it's likely your Mum, who would back down, so talk to her or suggest your DF does, beforehand if you feel it's necessary.
I do hope that even if you don't take my advice, you are able to make your sister see sense, as otherwise this poor little boy is going to suffer through bad parenting, which is not his fault.