Monitoring software...

A property management software company performed a major software upgrade on a client's server of hours back in July.   My client has actually deemed it a "downgrade" because, the upgrade has caused the server to become unstable and crash frequently.  My client even went to the extreme of replacing the server with a new server and a clean installation of Windows 2012 R2.  However, as soon as the management property company reinstalled their software platform on the new server, you guessed it, the server began crashing again.  
The property management software company recently  requested total remote access to the server and, you bet I'm reluctant to grant this kind of "open-season/free-reign" access to them.  This said, their request for full remote access raises my concerns ever so more since, they've disabled most of the Windows Server 2012 R2 firewall features and have repeatedly edited the registry when I've manually monitored them on the server remotely.  Yet, this software is the only one that knows its own software better than anyone else, right!
While I'm aware of the built-in auditing features, I believe video capturing would be even more precise.  Can anyone make any recommendations for video capturing a server's activity for at least of couple of days?  Software?  I intend to allow this vendor access to the server for up to 48hours and would very much like to capture their remote access activities.   I've used TeamViewer successfully to capture video but, someone from our end must remain logged into to TeamViewer in order to capture the entire 48hrs and moreover, if the TeamViewer connection is severed for whatever reason, it automatically locks out the user logged into the server.