Someone emailed support with a similar problem, having DS4Windows set to turn the Dualshock controller off after 5 minutes of inactivity (using Bluetooth). They found that if they hit the PS button to turn it back on and moved the left stick (or IIRC any other input) within half a second it would reconnect properly; if there was no input within half a second, the game would treat it as a second controller, and bring up the profile selection window for split screen co-op.
Try that with the Steam controller.
