Missed Base Appeal with a Twist

[Manny A]

Sitch: Runners at first and second, two outs, full count on the batter. On the pitch, both runners take off. Batter hits a base hit into right-center field. R1 from second should score easily, and R2 from first is a speedster who thinks she should be able to score as well. However, R1 rounding third stumbles a little over the bag. Suddenly, R1 and R2 are both heading for home not very far apart from each other.

The throw from F8 to home is a frozen rope that may get R1, but the ball bounces in front of F2 and scoots by her as she puts her leg in R1's path. R1 tries to slide into the back side of the plate, but goes past home without touching it due to F2's leg. PU signals Obstruction as F1, backing up the throw home, fields the ball. She tosses it back to F2 to make a play on R2, but R2 slides into home under the tag just before R1 has a chance to recover and touch home herself.

You're the PU. If the defense appeals, are you really going to rule R1 out for failing to touch home before R2 scores, even though R1 was clearly obstructed from initially touching it?