You don't need to get their permission. Just install Linux (mint or any other flavor) and they will get used to it. Did this for a bunch of family members and after a few weeks of transition nobody ever complained after
I suppose I could do it when I come down and visit when they’re not looking, though I think they would be pretty pissed if I did that.
Hah, one could lie and say "Inside this window called Virtual Box is what Windows 12 will look like, it's a chance to learn it!".
If I installed a VM for them, they would use it exactly once, right after I installed it for them, and then never again.
Heh, "not children" but you complain about having to coddle them and their childish incapability/unwillingness to learn. Meh, enjoy your problem.
While I do find it really irritating that they refuse to leave Windows and I do find their unwillingness to learn new stuff about computers infuriating, I do get it.
Linux has gotten a lot better and easier to use now, but historically there's a reason that it has been associated as a "nerd operating system". Prior to about ~10 years ago, desktop Linux was decidedly unpolished and difficult to use. Getting video and audio drivers working used to be a long and difficult ordeal, package managers were non-intuitive, and we hadn't fully gotten the "web apps have taken over the world" state that we're in now. I've been running Linux for like the last fifteen years and for quite awhile Linux had a well-earned reputation of being hard to use, and I think my parents are afraid of that.
It's gotten much better now, and I think a lot of people could pretty easily migrate without too much issue, but I can't completely blame people for still thinking about how crappy it used to be.
If you don't want to be sneaky about it, just install it next time Windows craps itself.