From home to work does not require any port forwarding. That would only come into play if you were trying to access your home computer from somewhere else. Actually, I would encourage you to remove the port forwarding because with it on you are allowing anyone on the internet access to attempt to hack your computer (depending on the setup).
It is more likely that the firewall at work (I hope they have one) is blocking your connection rather than your equipment. Why is it only blocked when you use the router? Hard to say, but my assumption is that when you use the hotspot you have a different public IP address than when you use the router (I am assuming here that your mobile hotspot connects to a mobile carrier and your router is...