In-wheel motor (IWM) vehicles offer a more sporty driving experience but suffer from left-right torque differences that impair straight-line driving stability. This paper proposes an integrated yaw-rate control strategy for IWM vehicle based on adaptive sliding mode control (ASMC) to enhance both agility in cornering and stability in straight-line driving situations. Given that 1) internal and external driving conditions such as driving maneuvers, road surfaces, and unwanted external disturbances affect vehicle yaw dynamics and 2) the tire cornering stiffness and understeer gradient are decisive parameters in yaw dynamics, the proposed strategy adapts online to these two parameters. Moreover, the proposed strategy adopts an adaptive update rate during the adaptation process to ensure robust disturbance rejection performance under various driving conditions. All control laws are defined solely based on measurable information in mass-production vehicles, without any knowledge of road-tire conditions or uncertainty bounds. In experimental tests, the proposed strategy shows improved control precision, accuracy, and robustness compared to PD controller and non-adaptive SMC. As a result, the proposed adaptation strategy improves the maneuverability of IWM vehicles in both dynamic cornering and straight-line driving situations.