I think you are coming from a good place. But this is your day dream not hers. "it's not her year" what is going on with her? Maybe she can't do it. Maybe her job is on the line and she can't push it at work. She told you what she could do, and you're mad because it doesn't fit what *you* want. That doesn't seem fair to her.
" but I think she could try harder" Maybe should could try harder and maybe she couldn't. Maybe she doesn't want to. I don't think having your brother strong arm her is really in the right spirit of this.
And if she's always the family member that is difficult, you should've anticipated that when you decided to plan this.
Find a solution:Maybe you could Skype her in on that day?I don't think it's worth it to get mad at her. You're going to have compromise or do it without her.. In any event, it's not going to happen the way you fantasize about it.
You're not going to like what I've got to say about this, OP.
Since it seems like this sister sees your parents fairly regularly because she lives in the same town, why don't you and your other siblings plan to join your parents in AZ without her?
Insanity: doing the same thing over and over again and expecting different results.
. -Albert Einstein
Holidays are really, really difficult times to coordinate in this modern day. The Norman Rockwell image of the whole family gathered at the table has caused a lot of anxiety for people!
My suggestion is this: Choose another season to gather: this fall, next spring, next summer? It can still be a great celebration for your mom and will take the pressure off of trying to do it over a holiday. And when you can agree on a timeframe accept the fact that someone may not or will not come. If you let "making" your sister or anyone else in the family a condition of this being a happy occasion, you'll always be disappointed.
As for her upcoming milestone birthday - do something special like collect family photos and make a special scrapbook - or get her friends to send you cards or written notes about your mom and put those in a special keepsake book to present to her. You can do that with your own kids (you and your sibs) to give her a special birthday gift from her grandchildren.
If you can still make the trip at Christmas - then go and celebrate the holidays with your mom. Just don't simmer over who's "not there."
Your idea for the Christmas surprise was a lovely idea, but its clearly not coming together so let it go. Instead of being mad at your sister put your energy into finding another date that all 4 of you can get there. Like someone else suggested, maybe it could be in the summer, or not at Christmas but another time while they're still in AZ. Given your mother's age, I would try to do this sooner rather than waiting until the end of the year--like you said, you never know when things can change. Then for her birthday you could give her a digital photo album with pictures from the reunion plus pictures of all of her grandkids.
Just wondering, why do you accept that your brother cannot take time off until Dec 25 but don't accept it when your sister says that she cannot take time off?