In jeopardy after touching home?

[Dakota]

R1 advancing from 2B to home. She scores. She thinks she missed 3rd base, but in fact she touched 3rd. She retouches home and attempt to return to 3rd and is tagged before get reaches third.

Is she out?

Change the scenario slightly.

ASA 10U R1 advancing from 2B on a steal attempt. Ball from F2 is overthrown and goes into LF. R1 advances to home. She scores. Coach sends her back to 3rd, since she was not eligible to advance home on the play. She retouches home and attempts to return to 3rd and is tagged before get reaches third.

Is she out?

Explain.