Well, I can totally relate to your situation, except for the fact that I am a man. I too am divorced, and have 2 kids that I have been raising on my own. I think that, for you, it might be easier to get back into dating than for someone older (I am 39). At my age, many people who are single have already raised their own kids, and don't want someone who has kids. Either that, or they never had kids, and don't want any, even if they are not their own.
I think that for you, because you are younger, it won't be as much of an issue. Some good things to try to find a nice guy might be church, or possibly doing some volunteer work. Also, if you want a truly good guy, you have to be honest with yourself, and give one a chance. I have heard a lot of women say they want a nice man, but all they really go for is the studly guys with great bodies and big egos.
And as far as viewing men the way you do, that will just take time - and maybe some counselling - to change. For me, it took some good counselling to get over my hatred of women. You may find it could help you too.
Good luck : )