There will be a diagnostic fault code stored in the ABS computer. Having that code read will get you into the circuit or system with the problem. Based on the problem occurring related to turning, the first suspect should be the wiring for one of the front wheel speed sensors, however that shouldn't make the red light turn on.
The red light turns on in response to low fluid level, unequal pressures in the two hydraulic circuits when the brakes are applied, or the parking brake pedal is not fully released. The yellow ABS warning light turns on when the red light is on because the reason for the red light could prevent the ABS system from functioning properly.
Try pulling up on the parking brake pedal. If the red light goes out, the cable could be stretched and in need of adjustment, or one of the rear cables could be sticking and not retracting fully and pulling the pedal back up all the way.