Help me understand the BU positioning on this play

[youngump]

R1 on 1st, B2 hits a liner to center. F8 fields it on a hop and throws to second catching R1 rounding too far. R1 starts to go back and then instead moves toward third. The rundown is on and PU comes up to get the third base end of it.

Here's what I did and why I think it's not right. So on the hit I button hooked in and cheated toward second. So at this point I'm probably about 10 feet in and just a little bit off the line between home and second. This felt good for the throw in and I think would have been a good place to adjust to the play at second if it had occurred and been close (by moving toward the 1B-2B line). Since it turned into a run down, I ended up moving to bracket the run by moving toward third and toward left field a little. R1 gets tagged toward 3rd and PU makes the call. At this point, I convinced myself I didn't like what I had done because at no point was I really aware of BR2 (who inexplicably did not go to second on this play). But if she had gone to second, I don't know that I would have been at all in good shape to make that call. So what should I have done.