Op you are living with an abusive man. He doesn't care about your feelings or your children's, or he wouldn't act the way he does. He controls you and the whole house by moods, sulking, withholding agreement to things, refusing to engage with arrangements, intentionally spoiling special days, and making you think you are are somehow at fault.
He's done this for so long that you actually believe that you are in some way at fault. But you are not. There is nothing here to suggest that you are over-bearing and controlling, not a thing. He is accusing you of being what he actually IS. This is another part of his control - to make you think you are deeply flawed, which makes you more insecure, which means you won't leave him. And he does't want you to leave - despite his poor behaviour - because he enjoys having control in his house, and someone to play the 'wife' role, and the image that gives to the outside world.
He is making your life miserable and making your children question you and the situation. For their sake and yours, you need to get away from him.
You say that you worry what other people will think. I do understand that, but is what other people think more important than your children's welfare? and yours? And in any case, if people have always known you to be a truthful, decent person, why would they not believe you? I have had 2 friends divorce who didn't tell anyone they were being abused until they left their DH. In both cases, noone questionned their word (except perhaps the immediate family / closest friends of their DH, although I suspect they also knew it was probably true, but they didn't want to engage with them anymore anyway).
Keep seeking support here, and start making enquiries IRL about what you need to do, what your financial situation would be if you split.
And keep building on your relationship with your DCs. Be the loving, kind, supportive, positive mum that you've always been. They will see one parent being happy and supportive and one being moody and sulking. Which one would you want as a teen?