enet_host_broadcast will send a packet to the local network for everyone to receive if they're listening to it. I don't think that's what the OP wants.
The ENetPeer is the main connection object representing the "other end," so I imagine this is valid until such time that the connection goes away. I don't know what kind of notification you get when it becomes invalid, though.
Are you sure? I just tested here (server running on NY based VM, clients running on my machine).