Hi,
I suspect it is a problem with the xml or some strange cross-domain security issue that jquery isn't handling particularly well. We are using a slightly older jquery version and a few of those warnings indicate that the LO is still pulling in some things from http rather than https.
If the LO works when not accessed via vpn then it is likely the latter and it's affecting the ajax loading of the xml.
If the base url of the install (in management.php) is http:// then this will most likely explain why it's not working when accessed via vpn over https.
You could try temporarily logging into management.php and changing the base url to start https:// (of course that will temporarily break http:// access) and then see if that works (remember to clear your browser cache).
John