1999 Dodge Stratus keeps burning up right rear brake shoes

Hi wamppj. Welcome to the forum. First check for a sticking parking brake cable. Both shoes should be touching the anchor pin on the top of the backing plate, AND there should be at least 1/8" of free play when you push the parking brake strut rod forward against the pressure of its anti-rattle spring. If you flex the parking brake cable near where it enters the back side of the backing plate, and the shoes move, the cable is sticking or adjusted too tightly.

Contaminated brake fluid is a possibility too although that usually affects the front disc brakes first. Rubber seals will swell in the presence of petroleum product and grow past the return ports in the master cylinder blocking them off. The trapped fluid will heat up and expand causing the brakes to stay applied while you're driving. Contaminated fluid generally is not the problem when just one rear brake is dragging.

Caradiodoc

The hose is a definite possibility too. To tell, when the brake is still locked, open the bleeder screw. If the brake releases, look for a metal bracket that is crimped around the middle of the hose. Open that crimp up a little with a pair of pliers. Rust builds up in there constricting the hose. If it feels like the bleeder screw is rusted tight and going to snap off, you can loosen the hose's attaching bolt just a little, then retighten it right away before air has a chance to get in.

Caradiodoc