Safety-critical networks often have stringent real-time requirements; they must also be resilient to failures. In this paper, we propose the RealFlow framework that uses commodity software-defined networks (SDNs) to realize networks with end-to-end timing guarantees, while also: (a) increasing resiliency against link/switch failures and (b) increasing network utilization. The use of SDNs in this space also improves the management capabilities of the system due to the global visibility into the network. RealFlow is implemented as a northbound SDN controller application compatible with standard OpenFlow protocols with little to no runtime overheads. We demonstrate feasibility on a real hardware testbed (Pica8 SDN switches+Raspberry Pi endhosts) and a practical avionics case study. Our evaluations show that RealFlow can accommodate 63% more network flows with safety-critical guarantees when compared to current designs and up to 18% when link resiliency (via backup paths) is also considered.