Maybe you could ask your counsellor about his approach? He will have reasons for doing things the way he is, and if you understand those reasons, you'll have a better perspective on whether to carry on, or whether to find someone else who suits you better?
I notice you get challenges here - about not seeing your H, stopping the dates, not paying his rent, etc etc - and those aren't things you want or feel able to do. Are they the wrong challenges? Or perhaps there's something about the dynamic of having a change of action suggested to you, and you resisting it, that works for you in some way - and the counsellor is refusing to get into that dance with you?
If your counsellor were to give you homework, what kind would it be? If you know what kind of things you want, can you set it for yourself?
I know what you mean about the sex. But you know, if it was just sex you wanted, you could go and get some with someone else. It's the intimacy, isn't it? Or being wanted? Or that familiarity? I imagine that suggesting a hotel - or even going to bed with him - would not give you what you wanted. He can't even commit to being open and honest with you in conversation, never mind physically.
