When you move the key, Spine tries to keep the handles on both sides. When you drop it on the other key, you lose that other key's left handle and you get the left handle of the key you are dragging instead. To do what you want, set the transition between the keys to linear. Now there's no handle on the left side and when you replace the existing key, the existing key's left handle will be used.
The logic to do the "right thing" as you drag keys around is probably the most complex code in Spine!
