Generally when I next a girl, I won't bother to meet up with them as I'll probably see them again somewhere in my circles.

Twice, girls have asked me why I left them and that I seem cold to them now. I'm unsure what line I should take here.

They always ask me for a hug. It seems like some sort of compliance test. Like give them a hug to know that anytime they want, they can come to me and everything will be ok. I wonder if I'm reading this right.

If I refuse to respond to their hug / play or whatever it seems so passive aggressive like I'm mad or something. If I'm like hey and give them what they ask (the affection) then it's feeding them.

After I next, and I see a girl again, I want to know what frame I should be giving them. I've nexted the girl, so my mindset feels like it should be that they now I am not bothered with them and will completely dominate them (for me giving them some control or power in a relationship is a reward).

Today my girl visited me (she knew where I was), asked why I left last night without telling her. I opened up a little telling her she was teasing me (kissing then turning cheek) and I don't accept that. She asked for a hug which I gave. Then we talked, I said we need a few days apart, blaa blaa some more and she was like "ahhh I didn't realise you were so bothered by that. you act like you don't care but you do.". Then we became a bit more touchy and started to play/dance. We went somewhere more quiet and started drawing (doing creative stuff). She then just left without saying goodbye which I find disrespectful.

Next time I see her (because we're in the same place), I'll push for sex and that is all. She needs to satisfy me for my sake. No talk. Nothing. I gave her too much.

The bitch acts like she did nothing wrong. Some more facts:
- She is pushing for monogamy. I generally ignore this or change topic.
- Feminist. Comments a lot about my dominance.
- First time in our 2 week relationship that she has refused my advances (during day we were kissing then she'd back off or start laughing).
- Absent father figure, early boyfriend cheated on her.
- Attention whore.
- Talks about wanting serious relationship, but responds more to sexual behaviour than romance.

I will now use this girl for sex alone unless I see a dramatic change in her behaviour (I will be a lot more harder on her now). I'd appreciate comments on how I handled this for next time. Thanks.

After a next don't hold resentment or put them on 'thin ice', just go back to being your relaxed, positive self. If she wants a hug or some affection there's no reason to not give it to her. If you see her during the next just be friendly and don't discuss the next. Deflect (nicely) any questions and then resume the next afterwards.
verbalizing the next or the reason for the next is a bad idea, just makes you come accross as pouty/bitter. Saying 'you did x which I don't like so we shouldn't see eachother for x time' is pointless.