Disclosed is a system comprised of different points-of-presence (“PoPs”) that provide software defined hybrid private and public networking for different entity sites. A system PoP may establish and/or maintain different network circuits for accessing different destinations or services. The system PoP may receive a tunnel creation request from a particular site, may obtain entity-defined policies that are specified for the particular site, and may establish a particular network tunnel to the particular site. The system PoP may then route egress traffic with a first classification through a first network circuit with a different quality of service (“QoS”) than egress traffic with a second classification according to the policies. Similarly, the system PoP may route ingress traffic arriving over the first network circuit through the particular network tunnel with a different QoS than ingress traffic arriving over the second network circuit according to the policies.