Scenario from Adv. Camp
 

ASA FP Rules only

R1 on 1B, 0 out. F1 leaps on the pitch, called by 1BU. On the swing, B2 contacts F2's glove. The ball is hit into a 6-4-3 double play.

What do you do?

If the offense gets the choice of the IP penalty or the result of the at bat, would they not also get to take the result of the catchers obstruction? Since all runners did not advance safely, batter is awarded 1st, all runners forced to advance move up a base. Place runners on 1 & 2, no outs.

If the runner gets to first (per the obstruction in this scenario) & all others advance (forced), then there is no choice, correct? Agree, place runners on 1st & 2nd.

I don't think it's automatic (I think R1 to 2nd, BR to 1st is the "likely" result in almost every case, however...) Given that the offensive coach has options on both, suppose he prefers moving R1 to 2nd and adding a ball to the count (suppose batter is his best hitter, for example). On the catcher's obstruction, he takes the result of the play - so he can then accept the IP penalty instead.

Enforce both... Illegal pitch first, then catchers obstruction.

Sequence is important?

Yes it is...

The problem here in enforcing the IP first is that we don't know if "all runners advanced at least one base" until the decision on the CI is made.

In this case, it doesn't matter. With a runner on first, if you enforce both penalties:
IP - R1 to second, ball on BR, THEN Catcher's obstruction: BR to first, R1 doesn't advance (not forced). The effect is the same as if you just enforced the catcher's obstruction (BR to first, R1 forced to second).

The fun would be if R1 is at second and BR retired at first. Now the two effects would be different. My take is that you have to enforce both - R1 to third on the IP and BR to first on the Catcher's obstruction.
(ASA has a similar case play in which both penalties are enforced: IP and HPB.)

Actually....
 

You don't know if all runners advanced on the CO until you enforce the IP. If the count would have been 3 balls 1 strike and the coach chose to enforce the IP, then we would put runners on the 1st and 2nd ignore the CO.

True as well.

What you going to do?
 

Both the CO and IP rules say that the coach doesn't have the option if all runners including the batter runner advance safely one base. The rules also say when a runner passes a base, the runner is considered to have touched the base.

With that in mind, I give you the following.

R1 on 1st. IP/CO is called; batter makes contact. R1 makes it safely to third. BR misses 1st but makes it safely to 2nd. Defense appeals. BR is called out. Offensive coach comes out asking for you to enforce the penalty for the IP/CO.

What are you going to do?

The runner may have passed the base, but they did not advance safely to the base. Enforce the IP/CO. (Similar logic to a 2-out BR who missed first and makes it to 2nd, appealed at first negating a run - run cannot score on a play where the BR is put out before safely reaching first base)

Well, depends rule code. In ASA/NCAA, there is no enforcement of the IP/CO, as all runners and the batter-runner obtained at least a base, therefore removing the option for the offense. Therefore, the play stands (BR is out on appeal, R1 remains at third).
A similar play happened in 2011 in a NCAA DIII regional, BR hits a double on an illegal pitch, but misses first. The defense makes the appeal and the umpire (properly) rules the BR out. Unfortunately, the offensive coach (who's pitcher was having IP problems of her own, but that's a different story) argues about the IP, and the umpires (erroneously) allow the batter to bat again.

In NFHS, the offensive coach always has the option if an IP is put into play, so in this case you can give the option of the IP, but not the CO (I'll concede that I'm unsure if the CO will be negated in FED ball, but I believe it is).