Hostgator is in the 'cloud' ... with those servers (like all cloud servers) they are normally opened to too much and the provider or server admins have to work on protecting.
And what of Erin's server? Same hosting?
This still involves networking ... and primarily when students are on the school network. Is the school network a 'lower education' ... K12? ... or a junior college/uni? School networks (at least here in Texas and US) are to provide filtering ... for student safety/protection - that's both in workstation/device browsers and in servers hosted internally.
The filtering at your school might be done automatically ... there is a network proxy ... unseen and not configurable by individual student workstations/devices. That filtering may have picked up on the IP address of your server on HostGator as being something not to be trusted. Thus certain actions ... like uploading to or downloading from ... is trapped by a rule of some sort.
Is your moodle server running https:// with a valid certificate from a Certificate of Authority ... think HostGator provides that as a service and is default.
Users at home don't normally have such setups ... although providers might use Open DNS resolvers which protects customers from errant URL entry in browsers.
Again ... you will have to talk to your network people at school ... anything ... ANYTHING ... I happen to suggest might be way off! No Vulcan Mind Meld possible!
'spirit of sharing', Ken