I think you have said that you can access your library from other devices connected to your home network? As I understand it you are talking about accessing your library from outside your home network via the public internet? On that basis:
- What exactly have you done to ensure that the external internet facing IP address of your home network is known?
- What have you done in terms of port forwarding from the external network to the PC/Mac running Calibre server?
If neither of those questions means anything to you (yet anyway!) then it gives a good idea of what you are going to need to do to get access from the internet.