Abstract: Edge clouds increasingly must co-serve privacy-critical streams (e.g., per-user telemetry, industrial control loops) and best-effort utility services (e.g., Large Language Model inference, Augment Reality rendering) on the same constrained nodes to meet tight latency targets and sustain utilization. Running them on disjoint server pools satisfies privacy but leaves capacity stranded because private demand is bursty; naive colocation improves utilization but cannot offer hard service-level agreements (SLAs) or data-residency guarantees. We present DynaHyEdge, a hybrid scheduler that 1) continuously partitions capacity between private and public domains, 2) enforces per-core time isolation with microsecond domain flips, and 3) uses event-driven admission to harvest idle cycles without preemption. This joint design maximizes on-time completion while provably meeting private-task SLAs, keeping sensitive data local and reclaiming otherwise idle compute. Experiments on real-world and synthetic traces show that DynaHyEdge raises deadline success rates, lowers latency, and increases CPU utilization over greedy, fixed-partition, and earliest-deadline-first(EDF) baselines without compromising privacy.