Well, I should not even be commenting since I know very little about cloud computing, but from my understanding, AC does not use a web-based interface but rather connects using RDP connectivity. But, I would think you would connect via an RD Gateway with an RDP client on your desktop. So, if there is any slowness related to RDP, it would either be on their end, which obviously, they control or on your end, and why would they not be able to tell you what the problem is? What would be different about your RDC client and another office's.
Just to clarify, there is a difference between SQL Server 2012 Standard and SQL Server 2012 Express (both 64-bit). The former will give you a LOT more RAM but will cost you a lot more in licensing based on how they do this with a SaaS. SQL Server 2012 Express or any Express SQL will only give you 1GB of RAM.
You also mention 49,000MBs of RAM in one post = 49GBs and then 49,000GBs of RAM, which is a ton of RAM especially since you say there is 29GBs available. This would mean you are using 49,111GBs of RAM. I would always state RAM in GBs.
Your bandwidth should be plenty using RDP. Given this guess by support ask them to remote to your computer and set up RDP so it isn't slow. I don't see how you made your RDP slow.
Otherwise, I would move your AC back to in house on a server you can control.
