When you have type b obstruction you let it go until all play has ceased or there is an out made on the obstructed runner before reching his protected base. I remember all type a turns b some years back but the fact is it is always one or the other. When you kill it as in your play then yes the throw to second didn't happen. You place to where you think they should be.

Pro interp:
Under this section of the obstruction rule, the obstruction is to be signaled by the umpire pointing
laterally at the obstruction while calling loudly and clearly, "That's obstruction." The ball is not
dead, however, and the umpire shall allow play to continue until all play has ceased and no
further action is possible (see exception in NOTE (1) below). At that moment, the umpire shall
call "Time" and impose such penalties, if any, that in the umpire's judgment will nullify the act
of obstruction. It is important to note that in cases occurring under this section of the obstruction
rule, the umpire shall not call "Time" until all action has ceased and no further play is possible.
NOTE (1 ): If a runner is obstructed under this second section of the obstruction rule, play is to
proceed to completion-even if it results in a play later being made on the runner who was
previously obstructed. However, if such a play on a previously obstructed runner results in that
runner actually being tagged out before reaching the base to which he would have been awarded
because of the obstruction, the umpire shall in that case call "Time" at the moment the runner is
tagged out. The umpire shall then impose such penalties that will nullify the obstruction, which
will include, of course, the obstructed runner being awarded the base to which he would be
entitled because of the obstruction.