I'm wondering about the father's attitude to you, Nana. This may be rubbing off on the child. It sounds as if HE doesn't show respect to you. This may be where the problem lies. And it does sound from what you say that the parents are confusing the issue by not being consistent in their approaches.
Our own children and their partners are quite strict about their children's attitudes to all their grandparents, ensuring that the GCs understand about respect. DH and I will not tolerate disrespect either. We make this clear and DH backs me up always. I am talking here about the DCs that we mind.
Lots of praise, love and cuddles for good behaviour. Explaining that rudeness and aggression (which many small children show occasionally out of frustration) are not acceptable.
Those who commented on the concept of consistent boundaries have it right, I think, although consistency between the 2 grandmothers' approaches is maybe not so essential. Children learn to deal with different rules in different situations, as this child shows by his good behaviour at school (which probably rules out ADHD and autism). Although from what you have said, the other GM has NO rules. I wonder if she is being a competitive GM, trying to be the most loved one.
I don't think young children are benefitted by having no boundaries. To me, one of the key things they need to learn is to relate positively to a range of people and knowing what is not acceptable behaviour is part of socialisation.
Finally, I would suggest that, although you are understandably upset by this child's nasty behaviour to you, you try not to show it. It is perhaps giving him some sort of power over you, just as he exercises power over his sibling. Easier said than done, I know.
I do really feel for you.