Hinged character attachments use a fairly simple dedicated code (directly in the animation system) that can only handle one-hinge attachments with joint limits (they don't even handle collisions with the character or with other attachments).
To turn on dangling for a particular attachment, one has to specify 2 planes that form the edge used as a hinge. Planes are specified in the attachment's coordinate space. The first plane is the one the attachment "lies" on in its resting state, and the second is another plane it contacts with. For the most typical attachment orientation, natural plane selection would be positive y, positive z (+y,+z).
Default attachment orientation corresponds to joint angle 0. The maximum rotation angle is specified as the "limit" property. Use the "damping" property to prevent the "pendulum effect" (values up to 10 are reasonable, but can go even higher when needed).
Note that the changes take effect only after you press "apply" button.
Explanation - How the planes are defined:
The axis of the local coordinate system can be seen as normals on planes with the same name. The +y Axis is the normal to the +y plane. the -y Axis is the normal of the -y plane, +z is the normal on the +z plane (see color coding in the picture below). In the example above, the +y and +z planes were chosen. The hinge axis is created between them.