The way to tackle this problem is just to imagine writing a Schrodinger equation for the whole system consisting of an electronically controlled coin-flipping device, the coin it flips, and the environment in which the coin flip occurs.

There's basically no prospect of a coherent superposition involving the coin flipper and the coin. If there's an ambient gas, molecular collisions will be decohering both coin and flipper. Any computational processes in the flipper which dissipate energy will cause decoherence. Even in a vacuum, the thermal radiation from both objects should be decohering them. It's very interesting that something as large as a buckyball can apparently maintain coherent superposition even though it's in a thermal state, but the larger an object gets, the cooler it needs to be, to avoid decohering itself through thermal radiation.

In short, the wavefunction of the combined system will be a superposition of divergent classical histories (wavepackets moving through vastly separated regions of configuration space).