The purpose of the "Delayed dead ball" is to allow other scenarios to play. In a dead-ball scenario, all play is stopped and the umpire enforces whatever rule is needed with returning runners to a base or awarding bases.
In a delay ball for obstruction, the defense may continue play and record outs on runners that have not been affected by the obstruction (in your case, the BR). The BR can be thrown out at second as in your OP.
If the throw was to third base and R1 was out, the umpire would then invoke the obstruction and call the runner safe after the play has ended.
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