You really shouldn't be doing any of this, both from an architecture standpoint and a UX standpoint. But... You don't need the second set of navigation controllers. They should use the push and pop of the root navigation controller just fine. Tab controllers in Nav controllers is bad. But Nav controllers inside tab controllers inside nav controllers is worse.
Edit:
If you want to fix the navigation items, you need to set them on the Tab Controller. It is the "current" view controller on the navigation controller and so it's navigation items will be what are shown on the navigation bar.