Some states have unisex restrooms at their rest areas/service plazas (NY renovated them over time and now has them at all service plazas on the Thruway, but I don't believe the humble rest stops on along the rest of the interstates in NY do), you might want to check to see if any exist in the states you go through. Barring that, you may have to exit the interstate and find a single user restroom at a McDonald's or such. Some truck stops also have unisex restrooms.
Most will say it is a stupid issue to worry about, but it is always good to be prepared if you are concerned, and find a way around the issue completely. Believe me, I don't take many chances, especially when their are minors in the ladies room.