Have only read your posts, @PennyLany, so I don't know what comments you've got already, but I imagine they'll be mixed. Or at least, my response to you is a little bit mixed.
I can see both sides. I think! You see her being financially comfortable / well off, and to you, that is privileged. Certainly, not having money gives you shedloads of problems. (Been there, done that.) But - and I don't think you've taken this on board - having money doesn't mean you don't have problems. It's just a different set of problems, with either the money causing the problems or the money not insulating you from the problems.
Let's look at her problems. Her entire life is going to be turned upside down, there is no aspect of her life that will be untouched by her husband's plans. His money is causing her massive problems / stress / worry. Do you really consider having your life turned upside down 'privileged', just because the gas bill is covered?
I know you said "To be clear, he isn't forcing her! She is able to say no and he'll find another solution, he won't drag her on a plane or leave her behind" - now think that through. She says no - what will he do? How will he react to his (presumably long-held) dreams being rejected by his wife? What other solution will he find now? What sequence of events will be set in motion? How will that affect their relationship? Sometimes, you can only say 'no' theoretically. She may feel unable to actually say no, having thought through the consequences her 'no' will set in motion.
"I want to be there for her but I can't help thinking this is a very privileged position she is in and shouldn't complain too much. AIBU?"
To be blunt - being well-off financially is only a privileged position IF your challenges and problems are all financial. Her problems are NOT financial. So, yes - YABU. VU.
"maybe it's just me and I need to explore the reasons why I feel the way I feel."
I think you do need to ponder your feelings a bit. I wonder if perhaps you have faced / are facing / are feeling overwhelmed by finances? That your own problems would not be so pressing if you had her money? Explore away, it's never a bad idea to know why you feel how you feel.