"stopping" does not appear because the button parses the entire CompoundExpression in the second argument. For example,

DynamicModule[{state = 1}, Column[{Dynamic[state], Button["Trigger", state = 2; Pause[1]; state = 3]}]]

only updates with "3". I'm not sure why you're using UpdateInterval in your dynamics. If the dynamic is only a wrapper, then usually you want that to update as fast as possible.

I would suggest using EventHandler. It's a lower-level function, but you can use it to separate out the updates to MouseDown versus MouseUp events:

EventHandler[Button["Trigger", Print["A"], Active -> False], {"MouseDown" :> Print["B"], "MouseUp" :> Print["C"]}]

In the above code I still use a Button so you get a similar interface, but I disable the button's action. By putting your "stopping" update with MouseDown and the rest in MouseUp, you should get your interface to update as you want. Better still, you can make the button not do anything except change its appearance when clicked:

Column[{  
    Dynamic[state],  
    EventHandler[Button["Trigger", Null], {"MouseDown" :> (state = 2), "MouseUp" :> (state = 3)}, PassEventsDown -> True]
}]

Thanks for the reply. Changing “Preemptive” to “Queued” does make my example code work as expected. My real code (see below) is a bit more complicated. In the first button I make a .NET call to a camera that will not return control until it captures an image or times out. To make it possible to interrupt the capture, the call is inside a loop. With “Preemptive” it eventually stops the image capture, but never shows the word “Stopping”. With “Queued” it never stops.

DynamicModule[
 {run = True,
  state = "    Ready"},
 Column[{
   Row[
    {
     Button["Arm",
      run = True;
      state = "    Active";
      myCam@StartAcquisition[];
      While[run,
       currentImage = currentImageXIMea[myCam, 1000 (*ms*)]
       ],
      Method -> "Queued"
      ],
     Button["Stop",
      run = False;
      state = "    Stopping";
      Pause[2];
      myCam@StopAcquisition[];
      state = "    Stopped",
      Method -> "Queued"
      ],
     Dynamic[state, UpdateInterval -> 0.25]
     }
    ],
   Dynamic[
    Image[currentImage, ImageSize -> 300],
    TrackedSymbols -> {currentImage}
    ]
   }
  ]
 ]