I used to do this with DH. If I were awake at 4am, for example, he would want to have sex. I used to think well if I get it over with, I might get to sleep for an hour or so, after. If not, I'll lie here awake with him wrapped around me for another two hours.
Like your DH, he would be in a mood if I didn't. He would tell me he couldn't help it, because lack of sex put him in a bad mood. So I would give in to keep the peace.
And I felt shit.
I decided to stop having sex with him if he was grouchy, or to keep the peace (a blow job when I was on my period, for example). I stopped having make up sex, as I realised it's very easy to manufacture an argument, to get the inevitable sex afterwards.
Another tactic he used was guilt. He would say if I loved him, I would do it. I started to say that if he loved me, he wouldn't ask me to have sex I was too tired for, or if I was tense about something else. And so on.
A big turn around was that we went to counselling. She looked at our childhoods. She told me that I didn't have to justify myself to him. If I didn't want something, I didn't have to say why, I could just say no.
As far as his childhood was concerned, she helped him understand that emotional blackmail is not normal. (It was his normal, growing up, but she helped him see that it's not a good way of getting what you want.) I had tried to explain this to him many times, but I think a professional saying the same thing made him realise I was right.
The thing is, my DH is not a bad person. But what he was doing was all he knew. It was what got him results. I forced the issue, as I changed my reaction to him. I didn't reward him for bad behaviour.
I have found it hard to forgive him for that bad behaviour, but I do recognise that it was all he knew. It was what he had growing up, and I had continued to enable it, over the years.
The big turnaround for us was me being prepared to leave if things didn't change. I'm not saying LTB, but be prepared to, if you don't want to live like this, anymore.