See if someone can help me with something:
My front brake on the right side hangs when I run forward, but releases instantly when the car goes backwards.
What could be wrong?

The car is a Dodge Pioneer in 1961.

 

Bad brake hose or sticking wheel cyl

 

Could be under adjusted causing it to overextend and mechanically bind. Too many things to guess at without pulling a drum and having a look.

 

someone told me that maybe it was the brake shoes which was placed at the wrong side. But I have to me that they are equal at both right and left side in the drum

 

If this could be the hose or Wheel cyl ought brake locked up even when reversing?

 

No ! the extra leverage could push it back.. Also check and make sure there are no rough spots where the brake shoe rides on the backing plate

 

Most of them are guessing brake hoses. so I'll probably see if I can find two cheap on ebay or here in Sweden that sells U.S. auto parts. Usually only be so expensive here, I think the hoses cost about 25-45 USD in a Swedish auto parts store.