Why does my dock keep moving back to my other monitor?
Solution 1:
You can summon the Dock on a different display by moving the cursor to the bottom of the desired display, and then continuing moving down. It may be possible that this is occurring when you inadvertently perform that action.
I answered a similar question: cmd-tab behavior on Mavericks with multiple displays.
Solution 2:
If you can't drag the mouse down due to stacked monitors, or due to some other resolution differences between monitors. Go to System Preferences → Dock → Position on screen → click Left, and the dock will move back to the primary monitor.
Then you can go to the Bottom screen and follow the steps to summon the Dock, and it will return there.
Solution 3:
Apple didn't account for the over/under monitor configuration, the overhang catches your cursor and summons the dock. In this case, the switching is constant and annoying.
One workaround is to put the dock on the side of the monitor, which will prevent the summon when the overlap catches your cursor.
Solution 4:
The action that summons the dock to the opposite monitor is not very intuitive for me. This is what worked for me.
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Don't hold the mouse button down. (When people say "drag" the mouse, that usually implies with the mouse button held down.)
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The target area of the cursor needs to be at the bottom area of the monitor which doesn't currently have the dock at a place where the cursor can't move further down, i.e. this doesn't work on vertically stacked monitors along the area where the cursor can cross between screens.
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Once the cursor is "blocked", pause a sec, then continue the motion downward. The dock will be "summoned" to this monitor from the other monitor. This works for vertically stacked monitors as long as there is some place where the cursor is "blocked". If not, the cursor will just move to the other monitor since it is not "blocked". If you have identical resolution monitors, this will probably not work per @Geraldus_US's comment below. In that case you probably need to either left dock or right dock per @Geraldus_US. Alternatively, unplug the auxiliary monitor and the dock will switch to the main monitor.