Catcher's Interference options

[Bfair]

Situation #1: R3. BR hits fly ball to the outfield. However, the BR's swing was interfered with by the catcher. Outfielder makes the catch after which R3 tags up and scores. Umpire invokes the catcher interference, awarding 1st to the BR and sending R3 back to 3rd. Offensive manager wants the result of the play instead. Fine! BR is now out and R3 scores. Play continues. Pitcher steps off mound and tosses to F5. They're appealing that R3 left too soon. Umpire agrees and calls R3 out!
Umpire agrees. R3 is out.

Just for the record: I assume it is now too late for the offensive manager to say, "I changed my mind! We'll take the catcher's inteference."
Agreed

Situation #2: R2. BR doubles. However, the BR's swing was interfered with by the catcher. Catcher interference is ignored and the play stands. Play continues with the pitcher appealing to 1st that BR missed the bag. Umpire agrees. Now what?
As you state, the infraction is ignored since runner and batter each advanced at least one base. The BR is out. Had there been 2 out before the play, BR is 3rd out and run scored by R2 is negated. The catcher interference nor the format of applying the rule does not relieve BR of his responsibility of legally touching the bases while advancing.

Just my opinion,

Freix