I agree with you about the WH's poor public relations/communications team. That's been the one truly weak link in this administration literally since GWB was inaugurated January 20, 2000. However, not knowing how the PR team is set up in the WH, I don't know who to point a finger at. Rove is the President's top political advisor. There is a separate communications director. Currently that's Dan Bartlett.
I firmly believe that the "culprit" is W himself. He doesn't like the "blame game" or personal attacks. He treats everyone with dignity (even the ones who don't deserve it). And he won't let his team fight dirty.
He's the strongest President we've had in a long time (since Reagan, for sure). If the PR wasn't going the way he wanted, he wouldn't be shy about changing it. He hired Karen Hughes to work on PR in foreign countries because he didn't like our image there. If he thought he could do better with a different sort of domestic PR, I have no doubt he'd do something.
He's not anyone's puppet.