How can it not be having an affect on your kids if their dad's not at home?
I don't know about any of the previous history but if you're not happy, you really ought to do something about it. And if you think that living on your own isn't for you and you're better off where you are, then you have to try and make the best of the situation you're in. That means talking and not just getting angry. You have yourself and your kids to think about.
Also, have you told him you don't think he's been supportive? If so, and nothings chaged then you have to decide whether you can accept him for who he is. if you haven't told him, then you should. How can he change if he doesn't know it's a problem - although if you think it's something he should just know he's got to be supportive about and he's not, then again, you decide whether whether you can live with his attitude or not.
Then of course there's the critising. I wouldn't be too impressed if my other half critised me. We'll tell each other if we think we're being stupid about something but never actually critise and visa versa. But that's just me. Maybe you give as good as you get, I don't know.