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This is good, I like the gif dump, it gives me a good indication of your progress. You have taken several twists and turns already, which is fine! I have also taken a turn in my project which slowed me down alittle. The swinging looks really good now. Depending on whether or not you want to emphasize the player's skill in clicking at the right time, or emphasize proper movement control will determine how you trigger the swinging mode. My personal preference comes from terraria which sorta has a grappling hook which is tied to the left mouse button. The grappling hook just shoots in the general direction of the mouse, that way the mouse doesn't have to be RIGHT on the hook-able object, instead the grappling hook just collides with it along the way.

Thanks for the advice! The Terraria example is pretty useful and practical. And thanks for pointing out the control vs freedom bit. I definitely want to swing wherever I want, and I'll make a way for it.