Mila, I agree, why would you need to go to a C to talk about business? Didn't you and H build up and run several successful businesses during your M? If you had trouble relating to him about it, I doubt they would have been successful.
You have told him you have no problem talking to him pertaining to business, yet he persists with this C issue. It is rather curious, but so are a lot of things they think and do during a MLC. It does sound like a control thing for him.
Being dark is a new tactic for you and you only. It's about your choice in this. (We do get some.) It's time spent in healing, self discovery, growth, GAL and anything else YOU want. So what if it has an affect on H. He didn't seem to concern himself with you when he took up with ow. Let him twist.
He told you that even though he was with ow now he could still manage his part of the business. Well as Jack said, you're a smart lady, I'm sure you can manage your half of the business while staying dark on the personal side of things. People do it all the time. Successful people know how to separate personal from professional. I have no doubts you could handle that very well!