As far as I know, you can't share your VMs remotely on Virtual Box. You can, on VMware Workstation.
You can of course install whatever remote server you want inside the VM but aside from that you can connect to a VM directly using VRDP.
But you can also manager your entire virtualbox instance using RemoteBox ( http://remotebox.knobgoblin.org.uk/about.cgi ) or from a web GUI using phpVirtualBox ( https://sourceforge.net/p/phpvirtualbox/wiki/Home/ ).
I'm sure there are other options as well.
I have played with both of the alternate solutions you have shared. These are not perfect, unlike what VMware Workstation provides (as it has, for long period of time).