Poor Execution Leading to a Loss

Let's call a spade a spade. The picture shows me playing in my third match (I'm the larger fellow in red) at the Herb Healy. I played a two knights defense which is an opening I play often and enjoy. I miscalculated what I thought was a mating net and overlooked a forced mating net. This error was played in this position with Black on Move. I made the poor move Rxg2 instead of the winning move Q-h3.




To view paste the game here
1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. d3 Bc5 5. Nc3 d6 6. Bg5 Nd4 7. Nxd4 Bxd4 8. O-O Be6 9. Nd5 Bxd5 10. exd5 Qd7 11. c3 Bb6 12. Qf3 O-O-O 13. Bxf6 gxf6 14. Qxf6 Rhg8 15. b4 Rxg2+ 16. Kxg2 Qg4+
17. Kh1 *

The overlooked proper play would of been this.

1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6
4. d3 Bc5 5. Nc3 d6 6. Bg5 Nd4 7. Nxd4 Bxd4 8. O-O Be6 9. Nd5 Bxd5 10. exd5 Qd7
11. c3 Bb6 12. Qf3 O-O-O 13. Bxf6 gxf6 14. Qxf6 Rhg8 15. b4 Qh3 {1} 16. g3 {5}
Rxg3+ {0} 17. hxg3 {0} Qxg3+ {0} 18. Kh1 {0} Qh3+ {0} 19. Kg1 {0} Rg8+ {0} 20.
Qg5 {0} Rxg5# {0} 0-1

While playing I wanted him to open my g file by his Bishop X knight then control the g file with my rook. I had miscalculated it a few times think my rook sac was unstoppable but did not see it. Clearly I should of spent more time and looked for better alternatives.

I spent the rest of the game a rook down. He built a strong attack with a pawn on the 7th file rook on a open file but had trouble finishing me off. It ended with me
winning back my rook, taking the pawn on the 7th rank,trading queens evening up the game. He then beat me in a rook and pawn endgame.

This is my thoughts to ensure better play:

1)Spend more time in key points of the game and calculate fully.
2)Solve more problems consistantly instead of alot in short spurts to improve vision. (toward that end I am solving a minimum of 5 a day with many days having more)
3)If I expect to play better in tournaments I need to play in more tournaments or play longer games in tournament like conditions. (unlikely I can commit to more tournaments)