1. A cloud-connector subsystem that provides a stretch-deploy operation for moving one or more virtual machines and virtual applications, that 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, 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 creating, from a first edge appliance through which the one or more virtual machines are connected to a first virtual organization network that is, in turn, connected to an external network, a secure communications tunnel to a second edge appliance through which the second local virtual network in the routed virtual application is connected to a second virtual organization network, in turn connected to the external 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.