I would do the ethical thing and explain the privacy implications of you hosting it but him hosting it too. Honestly I’d turn on end to end encryption.

You having their data and him having his family’s data is a big responsibility. You need adequate security both online and physically.

There’s also the fact that he has access to it if he’s an admin. Not everyone can handle that responsibility.

As to your original question, Nextcloud breaks often, relative to how often the server will have problems. You’d def need SSH access.

It would probably be better for you to get an ASUSTOR NAS in terms of hardware. It Supports apps and Nextcloud is one of them.

It also has support other than you, which depending on a few factors (magic 8 ball), might be more time consuming than you’d think. They may not want to deal with hardware either if something did occur.

From your diagram you should be able to access it already. It’s what is called dual NAT where a router is behind a router.

Otherwise you could turn off DHCP on one and use static IPs / routes

Would it be possible to plug your media server into both routers?