1. A cloud-connector subsystem that provides a stretch-deploy operation for moving one or more virtual machines and virtual applications, which execute in a source cloud-computing facility, to a target cloud-computing facility, where the one or more virtual machines and virtual applications resume executing, the cloud-connector subsystem comprising: a cloud-connector node associated with the source cloud-computing facility; a cloud-connector node associated with the target cloud-computing facility; and a cloud-connector server that includes one or more processors, one or more memories, one or more data-storage devices, and computer instructions that, when executed on the one or more processors, control the cloud-connector server to provide, in cooperation with the cloud-connector nodes, a stretch-deploy operation that: extends a first local virtual network within the source cloud-computing facility, to a second local virtual network, within the target cloud-computing facility, through a secure tunnel that supports multiple extended virtual networks, forming an extended local virtual network, by: verifying the source cloud-computing facility and one or more virtual machines and virtual applications to be moved, verifying the target cloud-computing facility, creating a routed virtual application within the second local virtual network, launching execution of the routed virtual application within the target cloud-computing facility, and when a secure tunnel has not already been created between a first and second organization edge appliances, creating a secure tunnel between the first organization edge appliance, associated with the first local virtual network, and the second organization edge appliance, associated with the second local virtual network, and moves the one or more virtual machines and virtual applications from executing on the source cloud-computing facility and communicating with other computational entities through the extended local virtual network using one or more network addresses to executing on the target cloud-computing facility and communicating with other computational entities through the extended local virtual network using the same one or more network addresses.