Your son (the actor) is giving different answers to you now, and seeming not to have strong feelings about it now (as you note in your SWH addition.)
But the play itself is still two weeks away, and while doing the play before audiences, your son will greatly intensify his bonds with the rest of the cast. He may be saying now that "it might be kind of boring" but once the play is actually onstage -- I think he very likely will be burning to go to that cast party by the time the show's run is done.
That is something for you to bear in mind as you keep asking him about it. He's going to feel differently about the party once the play is underway and as it reaches its end -- which is really a major milestone for him. And he's going to want to celebrate it.
Also, you managed to write an amazingly and admirably calm post considering all the tough things going on your family right now, mentioning that these things are causing you stress -- but not mentioning how that stress is affecting your own attitude toward your son's dilemma and decision. Do you on an emotional level feel you really need your younger son there? Is there a part of you that will feel hurt or upset if he's not an acolyte in, or doesn't even attend, this service? Is there any feeling of "the confirmation may be the last big family event where we are all together"? I hate to put it that bluntly, but you were careful in the post to separate his schedule conflict from the serious illnesses in your family, and I wonder if in your own mind there is some link like that.
I think you need to own up to any feelings like those -- privately, not with your son there.
And then: Still let him choose and be clear his choice is truly OK with you. Assume that he doesn't really realize just yet how much he WILL want to go to the cast party; and I'd prepare myself for him to do that and not be at the confirmation.
Don't let it all hang until the last minute; let him go ahead and say yes to the party sooner, not later. He likely is well aware of the stresses the family is under and is reluctant to add to any stress by saying firmly that he does want to do his own thing; he also may be feeling guilty because he perfectly well knows that not only his brother but also his mom have put a lot of work into the confirmation. But if he really would rather go to the cast party that he's earned, and do his own thing with his own friends, I would say, back him up. Not just "let him do it" but back him up, which means not letting brother or dad or anyone else in the family make comments like "You should be there at the service for your brother" etc.
Your son is not asking to go to a football watching party on that Sunday, or to go play laser tag with buddies, or even to go to a friend's birthday party. He's weighing whether to go to a party that marks the end of a commitment for him. So I for one think it's different from just blowing off the confirmation for any other party or event.
This kind of conflict is going to come up again, based on the ages of your kids and their activities.
Oh, I hope you ignore the earlier post about how your son's "selfish, sinful nature" is what is prompting him to want to go the the party. What an awful thing to say about a kid this poster doesn't even know. You know your son best. Go with what you and he work out, not with guilt and shame as that person would have you do.