You don't re-parent the parts, you change which polygons are in them. In the Poser Setup Room, each part of the figure's skeleton (conforming clothing is a figure) has an associated group of polygons with it. The groups need to be arranged so that no body parts touch unless one is directly parented to the other. Here's an illustration:

The lines represent polygons, and the yellow, green, and pink areas represent body part groups like they did in my last illustration. The gray polygons can either be added to the collar group (green) or the shoulder group (pink). If they're added to the collar, then the shoulder will only touch the collar, which touches the shoulder (parented to it) and the chest (the collar's parent). Everything should work fine. If the gray polygons are added to the shoulder, then the shoulder will touch the chest, and the shirt will probably "tear" when the figure moves. Does that help?