Unwanted Clip Editing. Please help! Hope this makes sense...

I think what you are describing is how take lanes work.  The overlapping takes are supposed to represent different takes of the same part of the song. Normally you would do your comping, selecting the bests takes for each part and then either bounce to another track or bounce to a single take lane.
 
If you then close the take lanes so you just work in the track view you can edit the track as it seems like you want to.
 
With take lanes open you can hold "shift" down and put your cursor towards the top of the clip or split point you are trying to edit and you will see a slightly different cursor. This will allow you to slip edit the clip rather then moving the split point which moves it for all touching and overlapping clips.