What you are describing is called a "Door Glass Run". It is made of fabric and often trimmed with stainless edges. There are small metal pop in buttons to hold it in place along the inside edge and as you say should slip into a notch on the back support and behind a tab on the bottom. I believe we are talking about the same item. With it not sliding down as far as it should, is it too long at the other end at the "divider bar"? (The metal bar between the side window and the vent window) Some of these replacement parts can be a real bear. I redid my entire truck but the most frustration I had was with rebuilding the door windows.