When applying the brakes the brakes the car starts to shimmy or shake. This happened in the past and my mechanik said that there was dirt in the drums and they needed to be turned.Since I lived on a dirt road this sounded reasolable even though I had never had this on any other car. They turned the drums and it solved the problem, but 2 months later it is doing it again, shaking when the brakes are applied.

I suspect that the comments that there was dirt in the drums and that they needed to be turned were intended as seperate comments. I’ve never seen a drum come off that didn;t need to have some “dirt” dumped out of it. The dirt is unlikely to cause shimmying.

One thing that is true is that “turning” drums removes material and lessens the ability of the drums to handle the heat they generate without warping. That may be what happened here.

It’s also true that the front brakes generally do 70-80% of the work when stopping, and of the front brakes aren’t working properly the rear brakes may take up too much of the work and warp. “Work” in brake-speak means converting inertial energy into heat.

I’d elevate each corner of the car (a lift is a gift from the Gods) and spin the wheel by hand while someone slowly applies the brakes. I’d be “feeling” for proper function of the front brakes and for which wheel(s) is/are not braking smoothly. If the fronts are working fine and it’s a rear wheel, I might want to replace the drums out of suspicion that perhaps they can’t handle the heat after being “turned”.

I’d also want to inspect the front brakes for even wear on the pads.

By the way, don’t be surprised if you discover a stuck caliper in front. I culled a construction site for firewood some years back, driving routinely through soft sand and dirt, and had this problem.