Base missed when retreating, then ball out of play

[mbyron]

The principle you need is called "last time by." When runners are passing a base, they are liable for not touching the base unless they touch it on their last time by. FED implicitly recognizes this principle in, for example 8.2.1C.

So, in your play 1, R1 fails to touch 2B on his way back to retouch 1B and the ball goes out of play. Provided he retouches 1B and touches 2B on his way to 3B for the award, he cannot be called out on appeal. Failing either one, I would wait to hear the appeal until after the award and then rule the batter out upon a proper appeal. The case is complicated by the possibility of both a retouch appeal and a missed-base appeal.

In your play 2, R1 still needs to retouch 1B due to the caught fly ball. If he can do that and still end up on 2B, his missing 2B on the way to retouch 1B is ignored.

In both cases, your R1 would have fulfilled his base-running responsibilities by touching 2B on the last time by.