The officer did an excellent job.
To nit-pick, well, as BBI observed, if one is driving, drive. I saw some teetering-on-edge-of-disaster handling of that steering wheel and long gun. If one cracks-up the patrol vehicle, before arrival, there is no arrival.
Handing the coffee to the passenger officer was a wise move; let him get the coffee secured.
One clue about pursuit/emergency driving: Keep one’s fingers, thumbs, hands, and everything else OUTSIDE steering wheel. Visualize those spokes being double-edged blades, that will chop off anything within the perimeter of the wheel. How does one remember to drive like way, during pursuits, and when en route to hot calls? Easy; drive that way all the time, every day, every trip. Why? It prevents “air bag face,” and keeps one’s fingers, thumbs, and hands from being broken, in the event of a collision. A steering wheel can spin violently, during a collision.
One reason I really valued our Tahoes is that I had plenty of room to get even the lengthy Benelli M2 from its resting place, to a diagonal position across my thighs, with just my right hand, while driving with my left hand. (The Ford miniaturized, make-believe utility vehicles, which I had to use at the end of my career, made it VERY difficult to maneuver a long gun while inside the vehicle, which was a significant factor in my decision to retire as soon as I did, rather than work another year or so.) I had a well-researched ritual chain of actions to get stopped, un-seat-belted, and out the door, shotgun-muzzle-first, without getting wreck-tangled.