"check engine" light and "battery" light are on at the same time

This sounds like your engine just died while you were cornering. Has this only happened once? Do you notice that the car seems to pull in one direction when you step on the gas and in the other direction when you let off the gas (not braking)?

I ask because this is sometimes noticed when a motor mount breaks. A broken motor mount can also put a strain on wiring when cornering and that can cause the engine to quit suddenly.