In jeopardy after touching home?

[AtlUmpSteve]

In scenario #1, the runner puts herself in jeopardy by returning to the base paths. She is out in the play you posed.

In scenario #2, the same ruling might be thought to apply. However, the approved mechanic is for the umpire to kill the play once the runner safely attains a base she cannot legally attain, assuming all other play has ceased. In your scenario, there are no other runners, so it would be appropriate for the plate umpire to call "dead ball" as soon as the runner safely touches home.

So, if the umpire kills the play, the runner must be returned safely to third. If the umpire does not kill the play (and the Rule 8.4-H does not require that dead ball be called as soon as the base is attained), then the runner is off base, and in jeopardy, same as scenario #1.