[linedrive2ss]

As the play developed, the PU should have moved to 1st base line extended, so he could oversee the run down and be ready for the play at the plate. As the runner and ball converge at the plate, he should have stepped up the 3rd base line a few feet, giving a better view of the tag/foot on base, etc... also would not have been screened on the dropped ball. As with any close play/collision: Pause, Read, React. Play's over: "Show me the ball. He's out!"
Base U did the right thing by turning with the ball once his play was over, but, when you see a dropped ball that was screened to partner, you should call 'Time' and trot on over (whilst your partner trots on over to you -- ain't nothin' goin' to happen until you say what's what, plenty of time) to inform your partner of what you saw -- nice and private-like. He then can confirm/alter his call.
I've never had a problem with a coach that came out (after a brief conference between partner and I) and did not accept: "Coach, we just talked about the very thing you are concerned about, because we want to make sure to get the call right. The call stands (or: My partner saw the ball on the ground, I was screened, the call is: safe)."
Meanwhile, of course, partner should have been closer at hand instead of wandering around after he convinced 1st base coach to let his manager discuss the play.
The opportune moment came when the coach backed off with his hands spread in appeal. Fine time to step in and mosey off a few feet with the PU and just tell him what you saw.
Also of course ... what's wrong with saying to a coach asking that you et help: "No problem, coach. Hang on a minute." And pat your chest to your partner. He trots in, you wander over: "You got anything on that play?"

Inexperienced umpire, a bit of ego creeping in, not enough time before the call, too agressive towards the coach -- and, yes, the "herding off by the BU was a bit much.
Coach should have stayed in the game. These guys forgot that our most important function if to get the call right.

The only time we are required to get help is on a check-swing ball. Any other time, if it helps us -- as a team -- get the call right, we should take the 20 seconds and let everyone at the field that we are not ego-driven, just integrity-driven.