1. A cloud-connector subsystem that provides a stretch-redeploy operation for moving one or more virtual machines and virtual applications, which execute in a target cloud-computing facility, to a new target cloud-computing facility, where the one or more virtual applications resume executing, the cloud-connector subsystem comprising: a cloud-connector node associated with a source cloud-computing facility; a cloud-connector node associated with the target cloud-computing facility; and a cloud-connector node associated with the new 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-redeploy operation that extends a first local virtual network within the source cloud-computing facility to the new target cloud-computing facility, forming a second extended local virtual network, by verifying the new target cloud-computing facility, creating a routed virtual application with a third local virtual network in the new target cloud-computing facility, launching execution of the routed virtual application within the new target cloud-computing facility, creating, from a first edge appliance within the source cloud-computing facility, a secure communications tunnel to a third edge appliance through which the third local virtual network in the routed virtual application is connected to a third virtual organization network, in turn connected to the external network, and executing a copy phase and a deployment phase; and moves the one or more virtual machines and virtual applications from executing on the target cloud-computing facility and communicating with other computational entities through the first local virtual network and a first extended local virtual network that extends the first local virtual network to the target cloud-computing facility using one or more network addresses to executing on the new target cloud-computing facility and communicating with other computational entities through the second extended local virtual network using the same one or more network addresses.