If R2 fails to touch third base while scoring, how is the run by R1 affected upon a defensive appeal?

The correct understanding here is that a situation where R2 fails to properly touch third base does not impact R1's run if R1 successfully touches home plate before the appeal is made. In baseball rules, a run is valid as long as the runner crosses home plate legally, regardless of what happens with other runners.

In this scenario, R1's run will count as long as R1 fulfills the requirement of legally touching home plate. R2’s failure to touch third base might lead to R2 being called out on appeal, but it does not retroactively affect R1's actions or make R1's run invalid.

Therefore, the essence of the correct answer lies in the regulation that each runner's status is independent in terms of runs scoring, provided the initial conditions for scoring have been met. Thus, R1's run is valid regardless of R2’s actions concerning base touching.