It probably falls through because moving physics objects by events or other behaviors forces Construct 2 to "teleport" the physics object in the physics world, causing it to skip collisions. You have to do everything with the Physics actions (setting forces, impulses etc.) for it to work correctly.
i will try this again with forces, but there is one position on the left where it really looks like a bug. as you can see, the bough stops turning or moving while dragging a stone. i did this for debugging purposes.
and when u drop the stone cleanly over the bough more left, over the second polygon shape point, the stone is being "turned" somehow and falls right trough.
maybe someone here can give me more tips on how to solute this special stuff.