live ball appeal?

[umpharp]

Here is the play. ASA rules Mens Modified game

1 out with R1 on 3rd, R2 on 2nd, and R3 on 1st. Batter hits ground ball to F6 playing close to 2nd. F6 throws home (Why he didn't do the easy thing here and touch second? Who knows?) So F6 throws home and makes a bad throw that bounces off of the backstop. R1 scores but misses home plate. R2 rounds 3rd and starts towards home. F2 retrieves the ball and runs toward third forcing R2 back to third. F2 steps on home while doing this. Is that a live ball appeal on R1?
F2 has no idea that R1 missed home and did not step on home on purpose, but did clearly step on home while forcing R2 back to third.
F2 then throws to F5 and catch R2 in a rundown. R2 is tagged out after two throws.
Do we have three outs, end of inning. Or 2 outs and two on base.

Thanks.