My father is Jewish, my mother coverted Reform before marriage. My only religious/ cultural identity is that of Judaism. I married an Israeli 3 years ago. Can my children convert to Orthodox Judaism?
If they want to, yes they can... If your mother coverted before marriage, you ARE a Jew, regardless, so your kids are automatically Jewish. (I'm guessing from your screen name "Liza", that you're a woman.)
Why aren't YOU doing an Orthodox conversion? Your mother's Reform conversion is not accepted by the Orthodox, so to them you are not Jewish at all, nor are your children. As long as you are not Jewish I would not expect any Orthodox group to be particularly excited about converting your children. But they certainly are free to convert when they are of age.