OP here. So the "diagnosis" was that the brake was too tight. He loosened that brake and now it reverses normally. I don't know how the brakes get too tight when noone has worked on them, but $78 labor was not too bad and the problem seems to be fixed. Now, to get good tires on it.
BTW, we live in a very flat area, so I rarely use my parking brake. I actually call it the emergency brake, because that is what I would be more likely to use it for. If I park on a hill, I use it, but that just isn't very common in my everyday life.