The swaying out of control when going around corners or in wet conditions could be caused by several potential issues with your 2011 Range Rover Sport HSE. Here are a few possible explanations:

1. **Suspension Issues**: Worn out or damaged suspension components such as control arms, sway bars, or bushings can lead to excessive body roll and swaying during cornering. Inspect these parts for any signs of wear or damage.

2. **Tire Tread and Pressure**: Insufficient tire tread depth or uneven tire wear can result in reduced traction, especially in wet conditions, causing the vehicle to lose control. Check your tire tread depth and ensure proper tire pressure.

3. **Steering Components**: Problems with the steering system, such as loose tie rods or steering linkage, can contribute to instability when turning. Have the steering components inspected for any issues.

4. **Wheel Alignment**: Incorrect wheel alignment can lead to poor handling and stability, especially during cornering. Get your wheel alignment checked and adjusted if necessary.

5. **Braking System**: A malfunctioning or improperly functioning braking system, including worn brake pads, can impact the vehicle's ability to maintain control during cornering. Ensure that your brakes are in good working condition.

6. **Electronic Stability Control (ESC) System**: If your vehicle is equipped with an ESC system, there may be a fault triggering it to intervene unnecessarily, causing instability. Have the ESC system scanned for any error codes.

It's crucial to address these potential issues promptly to ensure the safety and proper functioning of your vehicle. If you are unable to diagnose or resolve the problem yourself, consider seeking the expertise of a qualified mechanic or automotive technician for further inspection and repairs.