Problems with religion in my relationship?

I am Roman Catholic and my girlfriend is a non-denominational Christian. Although she might not say so, she doesn't agree with Catholicism and believes that Catholicism split from Christianity. I don't think she knows the history or beliefs of us Catholics and we want children but she doesn't want them going to my church. I think it is more out of ignorance and not understanding of Catholicism. I just don't know how to explain it to her without her shutting me up or just not listening. I kind of get a "holier than thou" vibe and don't know what to do.