Any access to your sockets from the outside (using a mobile 3G or 4G network) still has to go through your internet router in order to communicate with the sockets. If they operate as intended while using the Wi-Fi network at home, the problem is probably not related to the sockets themselves, but to your internet router and how it interacts with certain requests.

In that case, get in contact with your internet provider so that they can check the settings of your router. Potential problems can be related to:
a) Ports being closed;
b) Coding of the security keys (WAP - PSK or WPA2-PSK);
c) Firewall settings;
d) Other encryption methods;
e) Parental security may also block connection;