This one is another of those "had to be there" sort of plays. The right call really depends on the timing of how the play at first unfolded. And the double first base complicates thing a bit, too.
The batter-runner seems to have been headed directly for the colored portion of the base. If so, then she is doing nothing wrong and is running in a perfectly legal manner. On this sort of play, with the ball coming from fair territory, the defense is obligated to use the white portion of the bag.
While a runner is generally expected to not crash into a fielder holding the ball, and to avoid contact if at all possible, on this play we have a case of the defense being where they are not supposed to be- on, or in front of, the colored base.
The only way this could be interference on the batter-runner is if she had lots of time to avoid the fielder but chose to crash into her anyway. That doesn't sound like the case here, as you say that she was "just barely beaten by the throw". If (and I'm just saying "if"
the throw had beaten the batter-runner by a wide margin and she willfully and purposely crashed into the fielder, you would have interference, dead ball, batter-runner out and the other runner returned to her last base touched (which would likely be second base).
Another "what if" to throw in here- if the fielder had not touched the white bag, that would mean that the batter-runner was NOT retired before the interference. You would enforce the ruling as mentioned above. On the other hand, if the defense had touched the white bag, then the runner interfered, you would have interference by a retired runner. In that case, if the interference prevented the defense from making a play on the other runner, that runner (the one closest to home) would also be out!
Was this obstruction by the defense? Possibly, but there again you would have to see the play. If the defense is blocking the orange bag AND this blocking causes the runner to alter her path (ie: slow down, veer away or otherwise try to avoid the fielder before she has the ball), then you can have a case of obstruction. Just going by the description, it does not sound as if the runner altered her path, so it probably wasn't obstruction.
Back to the play at hand: Going through it step-by-step, and just by the information given, I would call this:
- No interference by the offense or obstruction by the defense.
- The batter-runner would be SAFE because the defense touched only the colored portion of the bag, not the white.
Result of play: Runners at first and third, no outs...send in the next batter! (And you can see, depending on a host of little details, that ruling could be completely different depending on who did what and when they did it.)
As for the scoring, I'm an umpire, not a scorekeeper! I'll let the folks that handle that answer your question. It might be relevant to know how the runner who started out on first, and eventually scored, reached first base in the first place. If she did not get on by virtue of an error by the defense, I would have to think this run would be earned.