You might want to start with a couple overnights in the public car-camping campground - preferably one that doesn't have electric hookups, so you won't have to contend with RVs and loud yahoos next door. Use backpacking gear and menus, and basically live out of your packs, not the car - it's a very non-threatening way to get her comfortable and familiar with how the gear functions. If things go downhill, you can always head for the motel and plan how you'll do things different next time. You can carry your loaded backpacks on the short day hikes during these trips, which lets her get a feel for how to pack and how to hike with a pack.

Then head out on the overnight you described above.

Wish someone had given me the above advice out before I took my bride on her first (and last) backpacking trip.