I don't understand your problem description well, so it is recommended that you answer my following questions below. Besides, you can try to narrow down the problem.
1. Do the web sites work internally if you navigate to them on another internal machine? If so, then IIS is working without a problem and you don't need to change it.
2. Are you sure you have everything configured on your firewall/gateway correctly? For such networking questions, as they are out of scopes of this IIS forum, you'd better consult a network expert (for example, vendor of the firewall).
RDP has no relationship with IIS, so RDP works does not mean IIS can work (vice versa)