Driving with parking brake engaged

I have the same problem with my wife and my Darts. She can't pull on the handle hard enough to set the brake so when you drive away you can't even feel it.

This doesn't effect your front brakes at all so it isn't like you have no brakes, just be conservative. Me, I would drive it slowly (20 mph would do it) and try the brakes a few times - if you warped the drums you will feel it. That gives you more info for when you pull the drums and look at things. If they weren't on all that hard you might be able to replace the shoes and be good to go.