I'm not sure how much longer you could keep the Gallic Empire and Roman Empire separate. Both had as their end goal of uniting the empire, it's just that Posthumous realized that immediately marching on Italy would defeat his whole purpose of revolting-that being that the Rhine frontier was getting little support and was teetering on the brink of being blown fully open. Marching on Italy would have only exacerbated that problem. It was an eventual goal of his once he stabalized the frontier completely and sensed a weakness in the Roman Empire.
As for Palmyra...this is difficult as well. Once either the Gallic Empire or Roman Empire emerges victorious in the west, the winner's going to come storming east. The best case scenario for Zenobia is that that inevitable conclusion is delayed as long as possible. But the longer it is delayed, the better chance the Roman Empire stabilizes the Danube frontier (the splitting of the empire was a blessing in disguise I think. It allowed the legitimate Roman Emperor to focus solely on the Danube frontier, the Gallic Emperor to focus on the Rhine frontier, and Palmyra to focus on stabilizing the Persian frontier). So really, I think it will just be a matter of luck to have the Palmyrene Empire survive.
Now, if you really want a worse third century...don't have the Roman Empire split. As I mentioned above, the split was a blessing in disguise, and it may have been what saved the empire from total collapse. If it doesn't split, you'll continue to see a Roman Emperor struggling with the Sassanians completely overruning the eastern frontier, the Goths breaking open the Danube frontier further, and the Rhine frontier possibly collapsing (I mean, even IOTL the Franks raided as far south as Spain).
So how do you do this? Don't have Odenathus get lucky in the east and defeat the Persians returning from their decisive victory over Valerian, or have Shapur accept his gifts he sent him to placate the Persians, and he won't throw in his lot with Rome. Have someone more ambitious and less rational than Posthumous be in command of the Rhine legions and and declare himself emperor-he continues the time honored third century tradition of immediately going to fight a civil war. The cycle continues in other words as the Roman Empire falls apart.