This happens on multiple computers and multiple versions of maptool.
This is the odd thing. Maybe it's an OS thing... I suspect that different versions of java, video drivers, and operating systems probably change how things look while docking with swing.
For me, I have no problems docking, tabbing, and organizing my windows in MT (on multiple computers, windows platforms). But, I have had players that just always seem to have problems and when I see how they have their layouts poorly setup it's usually because they have trouble setting things up. With one player who complained a lot, I logged into his computer using remote assistance and had no trouble setting things up (even with the lag and low frame rate you get from remote assistance)... so, at least in his case, it was simply user error (and, yes, to this day he still seems incapable of settings thing up easily.)
In your screen shot it looks like you are trying to position the chat window.
1) Drag the chat window to the middle of your screen and size it down to about the size of a playing card.
2) Then, grab header bar (left click and hold) and drag it *very slowly* toward the Draw Explorer. What happens? In Win10 the Chat window stays in place and I am dragging an empty gray frame.
3) As you near the Draw Explorer, the "empty frame" you are dragging will eventually snap into a new orientation. If you let go of the left mouse button the chat window itself will snap into that orientation/position. You should be able to move the "empty frame" all around the screen, touching various other windows and edges of the screen to indicate different places you can dock the frame. Is this not happening for you?