Hi, Lawrence. It is possible to re-order the hierarchy by renaming items one at a time. For example:
Step 1--Rename as follows, in this order:
-Bucket (no change)
1) Program_old
-Initiative (no change)
2) Feature_old
Step 2: Rename top to bottom in desired order.
Be aware, however, that this could have major impacts in your organization. If people now call the top level a "Bucket," you will have to train them to call that a "Program" now. Any reports outside of Rally you have built referring to "B1" (or whatever your abbreviation is) will have to be changed to "P1." This would be especially confusing since you would be swapping the same names into different places.
The system is built to make the Portfolio Item field the "owner" of the order, not shared views. I gently recommend you change the views instead, and instead of sending out URLs, train people how to browse to the page they need. I'll say things like, "In the menu select 'Portfolio" and the view you want." That eliminates this problem. Good luck!