Is it possible that the hosts are trying to connect to each other from an address that is not registered to their hostname, for example, if your hosts are on the same LAN:
Resolves to: 184.108.40.206
Connecting from: 192.168.0.100
If MoodleTwo receives data from MoodleOne on the local network (from IP 192.168.0.100), and MoodleOne's wwwroot doesn't resolve to that IP address, then the data exchange will fail.
This can happen where only one of the hosts has an /etc/hosts file entry for the other, but some of my colleagues have also had problems when they've been doing interesting things with VServers, zones, etc.
I'm pretty sure that the libxml2 version mismatch is not causing the problems here, so I'd avoid looking to deeply into that.
I'm planning to add some code to this part of Moodle to offer users a less-strict IP address matching option, because it looks like this is causing problems for too many people.