If your rear brake shoes were provided by an aftermarket manufacturer, sometimes they provide both a leading and a trailing brake shoe. You have to be careful and make sure each shoe is fitted where is is designed to go. Maybe you have the leading and trailing brake shoe switched around and this is why the handbrake assembly is not working properly.
Take the shoes off the side that is not working and try to swap the shoes. Usually one brake shoe has longer pad material than the other, one is the leading shoe and the other the trailing shoe. Its worth checking out before trying to modify the handbrake assembly.