I'd have to say that the person who makes it through this life without some hard knocks and lessons learned is a rare find, and also that these kinds of women are missing out on guys like me who have learned A LOT about life through our struggles. We would make excellent spouses.
I'd certainly consider a Catholic lady who is divorced, with children, if she meets my other criteria. I don't get the feeling women feel the same about men.
At any rate, don't be discouraged. A real man isn't afraid to take on some level of responsibility for helping raise someone else's child(ren.) Look at St. Joseph, after all.