If you really have these convictions about her sleeping at your parents' house while you're in it, instead of having her sleep in the car, give her your bed and you sleep in her car. Problem solved! She can stay over whenever she likes, your convictions are intact, and you showed her a Christlike, manly gesture.
For me personally, I didn't have any problem having my girlfriend/fiancee who is now my wife stay at my apartment when she visited (we lived approx 270 miles away from one another). Visiting her, however, posed to be more of a dilemma because she attended a Christian college which had pretty strict rules. Whenever I visited her I had to stay with her brother in the dorms. He didn't much care for that.
Speaking of which. Why are you so opposed to visiting and driving the distance to see her? You don't seem to have a problem with her driving the distance to see you. Who cares what city you'll be in since the primary focus is visiting her. I'd go anywhere to visit my wife.