My wife rides an old Peugeot mixte that she loves. No matter what I do, I cannot get the rear wheel to sit straight. It has horizontal dropouts, so no problem adjusting to get it centered between the chainstays, but the wheel is invariably out of center between the seatstays. The difference is big enough that it makes fender and brake adjustment very difficult, plus it looks bad. I've use a homemade dropout alignment tool to verify that the dropouts are parallel and aligned to each other, and I've installed the same wheel in both orientations to make sure it's not an issue with the wheel either.

I'm sort of stumped. All the info I find online seems more focused on lateral rather than vertical alignment issues. There's no apparent damage to the frame, but it's definitely a cheap mass-market model that may have had loose tolerances for tube lengths, welds, etc. Is there some way to fix this problem, or is it hopeless?