Apple Time Capsule can be used as an internal hard drive. If you are using Apple Time Capsule Setup and want to share the internal disk while you are away from your network, then there is a possibility of doing that. However, if you are not seeing the checkbox related to that option, then there is definitely a problem.
You need to check if you set your router mode under Network to DHCP and NAT from the current off (Bridge Mode), then are you seeing the option of ‘Share Disks over WAN option’ or not. If you are, then you need to check if the internet works at that time or not. If not, then you are dealing with a major problem as most users are.
A DHCP server has the ability to automatically assign out addresses to any device that connects to a network. Private ‘fake’ addresses are mapped by the NAT server on the local network to a gateway address. The reason why I’m calling those addresses fake is that they can only work within your network.
The combination of DHCP and NAT on an Apple router will enable you to have one path to the internet that all the hardware can share without any configuration. It connects to the gateway and is assigned to a private address. All the traffic is routed to the broader world.
Bridge mode enables a router act as an extension of another networked router, which handles the address-assigning function. It could be the FiOS router, which might be handling NAT and DHCP.
With AirPort router not being able to manage the interaction with the rest of the internet, Apple decided to disable remote disk access along with barring remote configuration via AirPort Utility. Though, it is a bit weird because Apple has significantly relied on functionality that was present in MacOS for past several years, which has allowed users to share access from one Mac to another for screen sharing and connected drives when both devices are logged into the same iCloud account
One option for you is to turn the broadband modem into a bridge. Despite the fact that it is not allowed by all providers, plus the modem and network operator of every system will be different, so it won’t be possible to me to provide you any assistance on this. You need to check if your ISP provides any support to turn on bridge mode with its supplied router or the one you bought separately. After that, you can enable NAT and DHCP on Apple Wi-Fi base station that is connected to the broadband modem.
One more option that you can try is, enabling and coping with ‘Double NAT’. At that time, your modem makes use of NAT and DHCP, and a base station connects to the modem. With this, you can access all the NAT and DHCP features of an Apple base station, but you may also experience the two NAT layers preventing connections from the outside world from getting in. You will also get warnings from AirPort Utility regarding double NAT.
The 3rd option would be to install remote screen-sharing software on another Mac on your network, but only do this when you can leave your Mac running. You can use iTeleport to tunnel back in, which easily works via double NAT, especially for a screen-sharing session. Now, you will be able to access drives along with other items on the local network via a remote screen. Though the method is a bit complicated, it works for sure.