I don't know that I would suggest actually apologizing right now because as Trapt said, it most likely won't have an affect or could simply lead to a negative reaction which could backfire.
I would start maybe by writing him a letter, then if you choose to give it to him, or convey the message to him, you can do so. But see where you feel like you are. If it truly is something that you are doing for you, then you can give it to him.
Additionally, although you are apologizing, you have to find it in yourself to forgive yourself for those things that you think you did wrong.
His excuses, about the house not being clean enough, you not planting flowers, etc...Are just that, excuses. I, and others here, have heard very similar, if not identical complaints.
Look at what he has complained about, see what you feel really has merit and work on those things, if you feel you need to.
It sounds like you have a beautiful property. Maybe start making it your own a bit, flowers, a swing, a garden. Anything to keep this from dragging you into a depressive state yourself.
I think your position with the kids, whether they want to meet OW or not, is the right one because they really are old enough to decide that for themselves. Do not accept responsibility for them not wanting to meet her. As long as you are not stopping it, then you are not responsible. This is just the first of a long list of realities that he will have to face. He chose to do this, they choose to react how they do as a result of his actions.
You have found a good place and will find much support here. Welcome.
"Acceptance doesn't mean resignation. It means understanding that something is what it is and there's got to be a way through it."--Michael J. Fox