Control of an iPad from a home internet to another internet

Remote control of an iPad, and remote-accessing an iPad mic and camera, and remote-monitoring an iPad is going to be going against pretty much everything that Apple has built for privacy and security. That’s basically malware, if not authorized by the device user.

You’ll also have to either use existing tools that already drill through the inevitable firewall, or implement your own network connections through an intervening firewall.

Some of what is listed could be established using a HomePod and HomeKit sharing. Apple SharePlay allows content access, but not the remote monitoring and remote control features, as well.

Other parts of a solution might include Ubiquiti Express for Wi-Fi and networking and a G4 Instant for audio video. I haven’t tried remote VPN access into an Express as yet.

Closer to the price you’re aiming at is a purpose-dedicated tablet hardware that provides the required features, but that’s still going to have to contend with DRM content restrictions for music and movies for those aspects of this product.

This whole thing also needs to be carefully and thoroughly locked down, as unauthorized remote access into an assisted living facility might well be profitable for scammers and crooks

Ah, okay. I misinterpreted your comment about device-designing efforts. Doing this with your own custom tablet, or with customizations made to an Android tablet would probably be the usual path here, though that will may or will run afoul of DRM for any protected content.

For some of the existing not-Apple-related products, Claris Companion or GrandPad or equivalent might interest. As I am unfamiliar with the details, pricing and subscriptions, and security or privacy issues that might arise with those, you’ll want to discuss that with folks more familiar, or with the vendor.