Check for oil on the shoes - and is the cylinder going in-out ok when you press the brake? Slacken the handbrake cable, and then tighten the adjuster to bring the shoes in light contact - only THEN do you now tighten the cable to get the lever where you want it. It should lock both wheels at 20 mph on a dry road.....
Support the back axle, remove the back wheels and check that the ends of the cables are moving freely, apply some oil to the ends of the cables.
Adjust the back brake shoes and replace the wheels
Apply the handbrake and check that both wheels are locked, if not then release the handbrake and adjust the cables.
Apply the handbrake, check again and release the handbrake one notch. Check for equal resistance on both wheels.