I had a house mate who used sulking and silent treatment (I'm aware that is a different situation since it was a house mate situation). It wouldn't be anything to do with me as far as I knew. She would return from, say a weekend at home, and be in a sulk, and not speak to anyone, for days on end, bar those she had to interact with at work.
I was away for a few days, the second time she did it, and when I returned she asked where I had been, and told me magnanimously that she was wondering where I was, as she had just decided she was going to speak to me again.
I told her plainly, that I wasn't prepared to be treated like that. I didn't think of any of the wonderfully witty phrases that get trotted out regularly on MN. I just said it calmly and clearly. She didn't do it again.
Sulking is a horrible trait, it's not cute in a child, and it's run for the hills behaviour in an adult, especially in a partner, someone who supposedly loves you.
I can fully understand how a sulker, bit by bit, forces their partner into accepting their behaviour. And can switch on the charm once everything is going their way. But it's abusive, and that's the long and the short of it really.
You're far better off without that in your life, OP.