Assuming you are using iMovie 10, when you drag a clip into the timeline it should squeeze between the two clips where you placed it without deleting any clips. Unavoidably, the other clips in the timeline, including transitions, will automatically be moved undisturbed down the timeline to make room for the inserted clip. Any audio clips that are connected will move with them. Also, any clips in the upper timeline, including titles, are attached to the clip below them and so they will move undisturbed as well.
Another way to insert a clip is to drag the new clip on top of the existing clip in the time line and hold it there for a couple of seconds. Then release and you will get a pop up that gives you option to replace, insert, and so on:
Are you saying that the above does not happen when you insert a clip? If so, can you describe what procedure you are doing to insert a new clip in the timeline and what happens when you try?
As a side note, if you want freely to move clips around you can put a black background in the main timeline and place your clips in the auxiliary timeline above it.
-- Rich