I'm looking for the shortest algorithm to rotate 2 corners without rearranging any other pieces location or orientation. For example, turning the Top-Front-Right corner clockwise and the Top-Front-Left corner counter-clockwise. My current best is 13 (formerly 16) turns, but would like to learn better if someone can share it.
R' D R F D F' U' F D' F' R' D' R U
The idea is to take out a corner from the top layer and put it back with a different rotation. This can be done in 6 moves (R' D R F D F'). Then you turn the top layer and do the same move backwards. The move backwards applies the opposite rotation to a different corner and restores the rest of the cube. Finally turn the top layer back.
It is possible in 12 moves (HTM) using
U2 R' B D2 B' R U2 R' B D2 B' R
U' B2 U L' F2 L U' B2 U L' F2 L
In QTM, 14 moves is optimal.
Found using Cube Explorer