The VPN to my corportate network is connected, but I can't install my printer

In most cases, this problem is handled by two DHCP servers that allocate IP addresses in different subnets. On the one hand, the DHCP server in the corporate network and, on the other, the DHCP server of the "managed router".

Suggested solution: You deactivate the DHCP function of the managed router. Then, the virtual desktops also get their IP address from the DHCP server in the corporate network and all are on the same subnet. So the virtual desktops should also be able to connect to the printers.