Raising Kids with Non-Jewish Wife
Question
Answer
Shalom!
Thank you for your question and thank you for being so straightforward and honest.
On the one hand, conversion for your girlfriend is not an option for many reasons. One reason is that conversion for the sake of marriage is almost always invalid. Another reasons is that an “anti-religious” person is obviously not attracted to the mitzvot of the Torah. Any conversion without full hearted acceptance of the mitzvot in invalid. There are other reasons, as well.
As an orthodox rabbi, I cannot, of course, condone any form of intermarriage, as well the children born from a non-Jewish mother won't be considered Jewish according to Jewish law. Furthermore, almost all intermarriages end in divorce, especially after children come into the picture. Save yourself the heartache. As you yourself said, the dual identity is impractical, and will, in fact, be a disaster.
Therefore, I recommend you put your current relationship on hold and explore dating in the Jewish community.