Yuck, the groping, the demands, the manipulation.
Sulking is deliberately manipulative, bullying behaviour. That's what it is and all it is.
There is a distinction between someone who hasn't got their own way and is sulking and someone who is upset and has withdrawn. One of them is trying to create a bad atmosphere to punish and manipulate the other person. The other is trying to stay out of the way until they feel better. The sulker will never want to discuss what upset them and how it could be dealt with differently in future (because they want to be upset, it's a tool of their control). The upset person will want to do this (though may find it difficult, if it's a very personal issue, or difficult to articulate) and will respond well to patience and sympathy.
If you want to stay with him, you need to try having a 'cards on the table' conversation about your mis-matched sex drives and what does and doesn't get you in the mood. Someone who cares about you and your wishes and feelings would have that discussion. Someone only interested in their own wishes and feelings would get annoyed, exasperated and angry.
I suspect he'll try to play the 'needs versus preferences' card, to make the claim that his desire for sex outweighs your wish not to have it sometimes (after all, you do want it at other times and seem willing enough to go along with it when you claim you don't - rapist's logic).
You need to be really clear in your own mind that no-one has a right to sex. No-one's sexual 'needs' create a reciprocal obligation to meet those needs, in another person. Sex is all about desire, on both sides. Offers of sex should always be met with enthusiatic consent, before anything happens. Remember, you are not a service animal, there to service his sexual needs. You are a person, with her own desires to have and not have sex. He offers, you can accept or decline (and vice versa). He is not in a position to demand or expect a sexual service.
If that means you're too mismatched for he relationship to survive, well, there it is.