That's funny I'm having the same troubles. I copied and mirrored several of the parts in my assembly, and now I need to adjust one or more of them separately from the other parts and change only one or two of them, not all of them. I'm just getting my feet wet with Inventor as well. I did some searching on this and didn't come up with anything yet but when I do, or some kind soul replies here, we'll both have our answer. I hope there is a way to break the relation or bust loose the contraints on the parts individually. It's probably something simple we just don't know yet. I have a 960 page user manual here (PDF) and I'm scouring over it now for clues.
OK- Quick update. I opened the part in the model browser window in the left side of my screen. I then somehow got into Derived Parts and checked for the help but didn't find too much there. Now here is where my newbie nature got me in trouble. Somehow through a series of clicks and such, Inventor Fusion opened up with the part in it. I did a Push/Pull operation on the end of it and it got longer by 1.2 cm (or the 12 mm I was trying to increase it's length by). I then exited out of Fusion without doing a save that I know of and now back in Inventor, my isolated part is there and it's 12 mm longer than it used to be and it didn't change the other parts along with it. I have to get back to you once I understand what it is I really did here.
The main reason I'm being cautious with this is that a few days ago, Mr. Inventor himself, JD told me that Fusion is too dangerous or complex for newbies to be messing around with. He also made reference that Fusion may be unstable in some way itself. Anyway, I will keep experiementing and as I learn more will post back.