When manipulating large stacks I have found it is best to do the following:
Expand the stack.
If you are moving concealed units out from other concealed units, clone the top concealment counter.
Shift Select the new concealment counter and each of the units you want to move out of the hex.
Select the bottom counter of the counters you have previously selected for movement.
Drag and Drop the selected counters.
This should grab just the selected counters from the large stack and move them, remaining concealed, into the new hex.
When moving a stack into a large stack, the moving units will remain on top. Top move them to the position you want, you can move each of the real units to the position you want with the down and left arrow keys. The down key will put the unit on the bottom, the left key will move it down one position in the stack. The right key moves it up one position and the up key moves it to the top. Do NOT move the top concealment counter until you have the real units where you want them.
Now you can move that top concealment counter (which could be above another concealment counter) to the position above the newly moved units using the arrow keys as before. If there is no additional concealment counter in the hex, you need to use the left arrow key to move it down one position at a time until it is just above your real concealed units so that the concealed units are not exposed. If they are all dummy concealment counters it will not matter since they have nothing to expose.
Expanding the stack and using the arrow keys is the best way to manipulate stacks. If you use the mouse you will be sadly disappointed with the results since that movement is considered by VASSAL as a move of the counters, not a readjustment of a stack, even if you are only moving in the same hex. It will then redo the stack on its own which can have various results that you do not want.
I will also add that if you have a stack of dummies and real units in a hex due to all the skulking or whatever moves you have made, I prefer to place the dummies on the bottom. It makes it easier to move them out without causing loss of concealment to the real units, never do anything to that concealment counter directly above the real units without clearly understanding what you are doing.
EDIT: Another tip, if you want to move part of your counters from a large stack into the hex to the upper right of your current hex (direction 2), never move them directly there when your stack is expanded. First move them into an empty hex somewhere to the left, then collapse you stack, and then grab your moved units and place them into the hex you wanted them moved to. If you try to move into a hex where the current stack has expanded into VASSAL can believe you are just moving within that stack instead of realizing you are trying to move to a new hex.