Find the Winning Move

Today I want to share a position where you are challenged to find the winning move. This is from a casual (I take these very seriously!) game I played recently and my failure in this position highlights two of my weaknesses. Also, I later went on to decline a draw and then lose, so I shouldn't forget that either.

Here is the position with black to move. Black has a very clear advantage after the winning idea is played.

The correct move in the above position was one of my first candidates, but I did not have a good enough vision to see what to do after white's response. I found it fairly easily when moving the pieces around, but not during the game when I had to visualize it. This is one of my weaknesses, I have a hard time finding a second move by a piece unless I am particularly thinking of moving a piece twice in a certain line.

Another weakness was highlighted by the move I actually chose. I had the idea that trading knights would be good for me because then I could easily gang up on the isolated pawn. So I played 1. ... Nh3+ 2. Kh1 Ng5 with the idea that I can trade knights on the next move and that if he moves the knight "anywhere" the d4 pawn loses a defender and I can take it. I have this tendency to think in this way -- "if he moves the knight anywhere" -- instead of thinking of what's the best place he can move it. Of course, I was disappointed when I saw 3. Ne5 cutting off the queen from d4 and now threatening Nc6 when the knight again defends the pawn, now attacks the h7 pawn and is on a monstrous outpost. Meanwhile, I have maneuvered my knight to g5 for no apparent reason.

If no one gives in the comments black's correct line of play, I'll post it here in a few days. (Don't just give black's first move! Say what black will do against white's reasonable responses.)