10" drum or Kelsey-Hayes

First, discs are superior of course but I think your brake adjustment might be suspect. I come from a time where drum brakes were normal and discs were rare. Your problem was a normal occurrence on misadjusted drum brakes. I think this is your case because you did not indicate that the car darts about when hitting bumps or wanders erratically driving straight and level which would indicate a front end issue.

I don't know your experiences so if I insult your intelligence, it is not intended. The problem is that it takes longer to describe the adjustment process than it takes to do it. I will pass on what I know to work. This assumes the brakes are in good working order as you indicated.

Put the car in the air because you must be able to rotate the tire when adjusting. Leave the tire on the car, this is key. You cannot adjust drum brakes with the drum off and you need the tire mounted because that is where you get the leverage to get the adjustment right. Using a brake spoon tighten up the self adjusting star from the behind the backing plate. Tighten the star adjuster until it gets snug. Now, here is where it gets to the point. Grab the tire at 9:00 and 3:00 and rotate the tire 90degrees. This part is hard to describe. You must turn the tire with an "AAARRRGGG". Not an ARG, and not an AAAAARRRRRRGGGGG. It should take a significant amount of effort to turn the tire but not totally locked up. It will probably be too loose. Adjust a few more clicks and rotate the tire again. You may have to do a few more clicks again until the tire is reasonably tight to turn. Then adjust the other three drums the same way to the same amount of resistance. Too much resistance is more forgiving than not enough. It just takes a few more miles for the shoes to loosen up. If your mother could turn the wheel, they are not adjusted adequately. Again, the key to good drum brake adjustment is equal but significant resistance on all drums. They will loosen up in about 50-100 miles, but they will be equal.

If you already adjusted your brakes in a manner similar to this, you have a different problem. My experience in the last ten to fifteen years is that properly adjusting drum brakes is a lost skill.