Not sure I understand.
You need to RDP to work systems from various remote locations. To do this you use a laptop.
Previously you could do this from your home wifi but no longer.
However you can still do this from other networks such as the pub wifi?
Most home broadband connections don’t limit outbound connectivity so you can usually connect to anything – connections the other way (into your network) are often protected by a firewall on the home wifi router but that shouldn’t be an issue here.
Can you connect to other RDP sites from your own network? Try connecting to 109.168.97.222. It’ll prompt for credentials (just type garbage in) but the point is you’ll see things happening rather than it just hanging/pausing/timing out.
It may be the firewall at your work that has some bizarre config blocking your ISP or home address but unlikely. However like someone else says opening RDP up to the whole internet is asking for trouble.