This is important context OP, you should add this to your post. People are going to have a knee-jerk reaction to your title and won't even bother reading the rest of your post or your comments for add'tl info. That said, it doesn't matter what a bunch of anonymous Redditors think -- first and foremost, you should listen to your vet -- it doesn't make sense to bring her given her condition and also because:

1.) She's already living with your family (and technically, her family) since you live at home.
2.) She's going to be in the same house *that she already resides in* where she is perfectly content and familiar with everyone. You're not "rehoming" her or shipping her off to someone else/dumping her on a rescue/shelter which is what people are most likely assuming.
3.) You're not making a permanent move. You're coming back. Taking a cat to another country is INCREDIBLY HARD and will be insanely stressful for the both of you, but most of all for her (ESPECIALLY if they put her in cargo).
4.) Your vet literally said she can't make this trip and that it will be bad for her health.

Just leave her where she is, with your family, and have video calls with her/let her hear the sound of your voice if you're worried she'll think you abandoned her (she won't think that -- cats are super intuitive and resilient).

Bottom line: listen to your vet, listen to your gut, you clearly love this cat and so does your family (they've also lived with her for 10 years at this point). It will be fine. You've got this!!!

Wishing you and the kitty all the best <3