I would agree with Warren's assessment, and add to that information this play from J/R:
R2, one out. The batter hits a pop fly to shallow right center field. Misplayed, the ball drops amidst three fielders. R2 is unable to advance and has returned to second. The batter-runner rounds first aggressively and is obstructed, but continues his advance to second without hesitation. He is able to reach second, and jointly occupies it with R2, when both runner are tagged: the batter-runner (following runner) is out. He must realize that R2 has not advanced. The obstruction does not give him license to ignore the actions of his teammate while advancing.
In your scenario, it is likely a Type B obstruction since the BR, after the obstruction, returned to 2B where the throw then came from left in an attempt to retire him. If the BR was legitimately advancing at the time of the obstruction, it would seem the throw from left would have been going to 3B in an attempt to retire him there if it had already been released. Fielders typically don't throw to the base behind the runner in an attempt to retire him at his advance base. Therefore, the throw going to 2B is an indicator that it likely originated after the obstruction and after BR's decision to return to 2B.
With Type B obstruction, you should nullify the act of the obstruction. Without R1 advancing beyond 3B, it was not possible for BR to safely acquire 3B. Even if BR advanced to 3B, R1 would be entitled to the base. With that said, there is no reason to advance BR to 3B even if he could have beaten a throw there because BR could not have safely acquired that base.
Had BR safely advanced to touch 3B after the obstruction, you would not award him that base if he was put out after discovering he jointly occupied it with R1.
Type B obstruction is not necessarily a free ticket to DisneyWorld---despite what many offensive coaches and players may at times think. It is not cause to protect a runner from his own stupidity regarding other factors occurring within the game.
Freix