Despite what others may have alluded to, there is currently no reliable way to control an ipad from any other device. I'd love for someone to prove me wrong.
Apple's "Switch Control" feature is an accessibility feature for people that cannot use a touch screen. I would highly recommend trying it on your own ipad first before assuming this is a possible solution.
The first barrier is that it's very annoying to actually use (being designed for people who cant use an ipad). The 2nd barrier would be the need for both ipads to be on the same wifi (this can of course be fixed if you've got a spare network engineer handy to set it all up for you. and stick around to fix any issues). The 3rd problem would be both devices need to be signed into the same icloud account. The 4th problem is that in my experience all of this is very very brittle in the best circumstances. Meaning it works very unreliably, if you can get it working at all.
Apple doesn't allow remote control of ipads. Personally I think it's a security feature (ipad is based on iOS, and it would be a gigantic security risk to allow someone to VNC into your phone). If you think about it, what's to stop someone else from getting your loved one to enable access and steal their banking data?
I know many people aren't going to like this and I'm not saying I agree with Apple (or disagree). It's a really tough situation to make secure and it looks like Apple is inching towards possible solutions that are lower risk.
That being said people need solutions NOW and forcing someone to use Android (or god forbid Windows) is certainly not a secure solution.
What Id probably recommend is
a) have a caretaker there you can facetime with. facetime will allow screen SHARING but afaik not screen control. if they aren't coherent enough for you to tell them to press a button or use any of the many many accessibility features themselves, I'm not sure how they can possibly be safe alone
b) use a Mac. this is fraught with many downsides, but if you can possibly put a keyboard protector on to prevent damage, you can set up screen sharing and do it that way. Mac is a far more mature platform with many reliable options for this. it's also very secure, and allows controlling the device via facetime or other options
c) if you're a network engineer, set up a VPN to get your ipad "on the same wifi" as the target ipad. should work, but also hacky and unreliable
d) if you're a hardware engineer, build a CNC using a capacitive stylus you can control remotely. tons of work, fraught with potential issues, but would be pretty dang cool