First we should understand that SCVMM Self-Service portal is using ActiveX controls to connect the remote VM.
The Self-Service Portal is accessed using Internet Explorer which requires ActiveX controls to provide remote access to virtual machines on managed hosts.
When a user uses the Self-Service Portal to view or connect to any of their virtual machines, they will be prompted to install the appropriate ActiveX control in Internet Explorer on their local machine.
Self-Service Portal will use ActiveX control VMMCtlAx and VMRCActiveXClient to connect with the remote VM, both ActiveX control are using RDP protocol to talk with remote VM.
Scenario 1: Opening SSP2.0 portal -> Virtual machine page -> Listing of VM
Status of SSP : Working
Reason: U1 tries to contact website which is possible. Website is able to talk to Engine machine and VMM hence You are able to see list of VMs.
Scenario 2: Connect VM Operation getting failed -> Open SSP2.0 portal -> Virtual machine page -> Listing of VM -> Try to connect
Status : Operation failed.
Reason: U1 is using machines from external world to connect to ssp.company.lcl -> Active X got installed on U1 machine -> for connect operation- This active X instead of going through Website directly goes to host for connect operation -> As Hyper V and U1 are on different network -> it is not working.
Workaround : You can check if somehow you can provide direct connection of host to U1 user machine.
Based on this behavior, we can learn that we cannot publish Self-Service Portal via ISA to connect VM via HTTPs.
Scenario of SSP on internet is not supported currently.
So what is the workaround for that ?!!! We can try solution like UAG
http://ahmedhusseinonline.com/2010/11/publishing-scvmm-ssp-using-uag-part-1-of-3/
http://ahmedhusseinonline.com/2010/12/publishing-scvmm-ssp-using-uag-part-2-of-3/
http://ahmedhusseinonline.com/2010/12/publishing-scvmm-ssp-using-uag-part-3-of-3/
Have a good day!
More info http://social.technet.microsoft.com/Forums/en-US/scvmmssp2/thread/b2a19b46-5ea6-42f2-bf80-18f35de8d927/?prof=required
Maheshkumar S Tiwari edited Original. Comment: Added Tag and minor edit