Most stable solution is probably to use Dante Via on both computers:
https://www.audinate.com/products/software/dante-via
Dante Via is capable of aggregating all audio sources on a computer (from connected USB interfaces and from running audio applications) and send them over the network (LAN, not WIFI). On the receiving computer, another instance of Dante Via routes the audio to vmix with fairly low latency.
Alternatively, you could run one Reaper instance on every computer and connect them via the ReaStream plugin (a sending instance on the sending computer and a receiving instance on the receiving one). You would then need to use free Voxengo Recorder plugin and a virtual audio cable to route Reaper's main output to vmix on the receiving computer.
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