How do I deal with a rude 12 year old nephew?

Call me harsh but I don't tolerate such behaviour - and certainly not in my own house!

Just cancel and explain why.

I’m obviously at odds with most posters. A 12 year old should know how to behave and when he is being rude.
If he were rude time personally , I would definitely tell him so and ask him not to do/say it again,
Mind you why his parents are not pulling him up on it I don’t know.

Whatever the situation if he was rude to me I would get up and leave, and then it is up to his parents to come to a compromise about dealing with him.
We have a child that visits who did this and we all decided to leave the room when he started. When he did which was during a meal we all just got up and went and watched T.V. he came through and after a short while, he started again, so we went back to our meal.
Being a teenager is no excuse but I think I would explain to his parents, especially the one who is not helpful what will happen when he starts. Also, tell him that you do not answer rude people and ignore him and go out of his way.I went into the cloakroom and locked the door.

There are several ways this could be approached and others may agree or not and present their own suggestions.
If you are likely to see him before they come to you after Christmas and he continues with his behaviour - you could make it clear to him that in your house that it isn't acceptable. Should he choose to act in that way then he can stay in his room and leave everyone to enjoy themselves without him. This strategy could also wait until he is actually at your house. Then plan to do things without him - if he hears everyone else having a good time he might just buck up his ideas.

If he says things are rubbish in conversation then look straight at him and say okay, now we are listening, tell us why you think it is rubbish and present his thoughts. He should not be allowed to say - it just is!! He is being given the opportunity to think and act like a young adult so get on with it!! He is being listened to - so say what he wants to say - no matter how ridiculous or reasonable his thoughts are. Listen to them and then have a conversation.

Unfortunately his parents are not 'parenting' if they leave him to carry on this type of behaviour. It seems as if he is attention seeking - and if he acts up like this at Christmas time then your niece and family need to be told that they need to pack their bags and head home. (And maybe warn her that this could happen!!)
He needs to understand there are consequences for unacceptable behaviour and if that means they remove privileges or recently given presents or everyone misses out because of him then he needs to feel the guilt for spoiling things for other people.

Please dont put your DH in the middle of this

Ignore
Leave the room
If he is directly rude to you and you cant exersize control over your own behaviour, try laughing and say how he reminds you of 'Kevin' on tv, then leave him alone
But ignoring is probably the best reaction.

I would phone the boy's father now and discuss his lack of comments on what both you and the boy's mother regard as rudeness.

I am not hinting, that the boy is not being rude, and apologise for my clumsy phraseology.

Most teenagers go through this phase of being rude and self-opinionated ( I know I did) and it will not get better unless the boy is kindly but firmly made aware that even if he does not intend to be rude, he is actually being rude and making himself unpleasant.

Reading your post, I wondered if the boy is acting like this because he knows that his parents are not in agreement about what constitues rudeness and is either trying to get a reaction out of his father, or trying to provoke his mother or you into losing your tempers with him.

Tell the boy's father that you find his son's behaviour annoying and you would like his help in dealing with it.

If he won't or can't see you point of view, there is little you can do, except what you already are doing.

If on the other hand the boy's father admits that he is at a loss how to cope, then you might be able to work out a strategy together.

I would let them come, having invited them. But you can, and should, get your husband to back you up if the boy is rude while staying in your house.

I take it ignoring the boy doesn't work, or turning round and saying, "Now we have all heard you, so please do not go on about this. I personally don't agree, nor do I wish to discuss the subject with you. And like Professor McGonagall from Harry Potter, I do not generally allow people to interupt me. Please respect this."

Most twelve year olds, I in 40 odd years of teaching have come across, do simmer down when told calmly but frankly that their behaviour is unpleasant.

Or they stay elsewhere and they leave when it gets unpleasant

I remember being dragged to visit family at that age when I really wanted to stay home and be with my friends

This of course is not your case but illustrating there could be a reason for his behaviour

The 12 year old is a teenager- being this rebellious is honestly not a surprise

I would cancel the visit if I were you

You know there are going to be issues and you and your dh cannot parent a child that is not yours.