Even if you had Nobles that wanted to War on each other, it would not work, since you would have anarchy across the Imperium. Not going to happen. Granted the Daimyo did it in pre-shogunate Japan, but once the Tokugawa's came in, all the local war stuff stopped, or the noble died. That is why you have the 47 Ronin. If you allow Nobles to war on each other, you have chaos, and an empire that falls apart at the first blow worse than anything GDW did with the Rebellion.
Local nobility is an entirely different critter. They will have their world or themselves as their primary concern and reason for being obstreperous. IN THEORY they are entirely separate from Imperial Nobles, who are supposed to be more concerned with the big picture. IN PRACTICE the Imperial Nobility can't help but be made up of local folks fairly often, so partisanship happens, grudges over past deals are unavoidable, and both Local and Imperial nobility are going to mix it up.
The Locals, being essentially planetary rulers, are covered under the Imperial Rules of War. The Imperium is not stupid, and knows that its thousands of member worlds are NOT going to get along all the time. The Imperium would rather everyone got along, traded back and forth, and made all parties lots of money. Reality is that people are frequently stupid, stubborn, vain, and proud, and have long but selective memories. Including the local rulers. ESPECIALLY the local rulers.
Imperial nobles are supposed to be above all that, but, shockingly, are just as Human (or whatever) as everyone else. The difference that sticks is that they are NOT covered by the Imperial Rules of War, but are instead bound by their oaths of Fealty to the Emperor. Their conflicts are *supposed* to stay in the boardroom, the Ducal or Imperial Court, or the negotiating table. Open conflict, either their own or being dragged into a local squabble, does not look good and will hamper their careers, and possibly shorten their lives, if discovered. So they try to stay covert. Industrial sabotage to force a contract you lost to go back out to bid; "lost" shipments (and ships) to make a rival look less reliable; social traps to make a rival's heir look like a liability to throw a succession into doubt; news suppression and enhancement; blackmail, extortion, and murder by proxy.