If, as you said, you've had the problem "since you had the car", is it possible that the leading and trailing shoes are that side are installed backwards?
In spite of what is often reported on the internet, in forums, and on car talk radio shows, etc., according to GM / Chevrolet service manuals, the leading shoe has the short lining. (e.g. This, according to GM 1966 sec 5-13, item 7, etc.)
Also, be aware that drum brake lining are eccentric by design. This eccentricity is not well understood by many technicians, and is vital to smooth brake operation. In a drum brake, the center of the lining first contacts the drum. Additional hydraulic pressure slightly deforms the shoe, engaging additional shoe surface. Again, this need for eccentricity is not well understood by a many folks, who simply presume that the entire shoe contacts the drum and that hydraulic pressure directly modulates stopping power. That is not true for drums. Drum shoes' braking force is amplified by the rotational force of the drum. Without some means of varying the percentage of shoe surface engagement, drum brakes would be "off/on" devices...which we call "grabbing brakes".
Therefore, The percentage of effective shoe surface engagement is modulated by the hydraulic pressure applied by the cylinder. Coupled with the eccentricity of the shoe, this is what provides variable stopping power on drum brakes.
Remove the linings and drum. Hand fit the linings into the drum on your workbench and examine them for slight eccentricity relative to the drum. Linings which do not exhibit sufficient / any eccentricity relative to the drum are highly prone to grabbing symptoms.
Here's a more thorough explanation, with pictures. See Pg. 9 at
Also, remember that the star wheels are L/R sensitive, and are so labeled. They are easy to get wrong. Correct adjuster operation is critical, as noted by others.
Finally, I have seen it happen where a car ends up with two leading shoes on one side and two trailing shoes on the other, due to the carelessness of the technician installing the shoes. A mixup on the bench results in the shoes getting jumbled together. This is also bound to cause problems.
Just some things to check