How to control a Mac remotely from a different network

My parents have recently gotten a Mac. To provide support to them, I'd like to be able to connect in remotely to their Mac from mine. I'm on a different network. I've tried following instructions to set up remote login and screen sharing, but when I've been attempting to take control, it has failed.

I know I could FaceTime them and screen share, however, I also personally have a Mac Mini, which I'd like to be able to connect to remotely from my MacBook Pro, so I wouldn't be able to FaceTime to that device, hence asking how I can connect remotely.

Any advice would be greatly appreciated.

Thanks