My hypothesis is that when recirculation is off, the heat is coming directly from the engine. When turning, the hot air is pushed to the side, leaving you with cold air.
I'm not quite sure what you mean by that. The source of the hot air, recirculating or not, is the heater core. Hot coolant from the engine flows through the heater core all the time, so it's always hot. The temperature of the air out the vents is controlled by moving internal flaps in the ductwork. When you (or the car) wants the air to be hotter, it diverts the air to go over the heater core. When you want just outside air, the heater ducts bypass the heater core. When you want something in-between 100% hot and 0% hot, the air is split and mixed in the right proportion. When A/C is turned on, the air flows over the cold evaporator coils.
This is in contrast to the way it used to be done, like back in the '80s. On my 4000, for example, the temperature slider actually moved a valve that throttled the coolant flow through the heater core. When it was set to cold, the coolant was prevented from flowing, and the core got cold. Turing the heat up opened the valve, and let the core get hot. But the heater core itself was always in the path of the air through the ducts. This had two major drawbacks... First, it took a while for the heater core to warm up and cool down. So temperature adjustments in the cabin were far from instant. Second, a valve in the cooling system is one more thing to break and leak. And leak they did! Since the newer system means that the core is always hot, and only selectively put in the path of the air, there's no need for a control valve. One less thing to break. As an added bonus, temperature changes are quicker, because the air responds very fast.
The first guess I maght hazard for the turning problem is that one of the internal flaps is moving with the lateral g-forces, and unintentionally bypassing the heater core. But that shoudln't happen turning both directions, just one. So actually, I have no logical explanation for this odd behavior.