VPN to RDP to a PC then to another VPN disconnects the RDP
Since the pandemic, we did resort to VPN-RDP to our office PC. This is required for security reasons. Unfortunately, whenever the user is on his RDP and tries to connect to another VPN the RDP gets disconnected. Do we have an option that the RDP will not disconnect whenever they connect to another VPN. The other VPN is Cisco Any Connect.
Yep, like @CptnCrnch said it sounds like based on the configurations of RDP machine and VPN clients you are disconnecting yourself. I have had this happen myself although more often when trying to leverage both wired and wireless connection on a laptop I am RDP'd to.
Depending on the network configurations and what you have access to make changes to it is possible in theory to make it work. I have sometime managed to create a simple static route on the Windows machine to help by forcing specific traffic one way or another to prevent being disconnected.
Cisco AnyConnect has an option "Allow Local LAN Access" which the head end you are connecting to controls. It is specifically meant to stop people doing things like what you are to preventing posting the destination network getting exposed to other unexpected uncontrolled source networks.
So I would say this is working exactly as designed by the company you are connecting to.