I understand that when systems are executing circular motion the resultant force acting on the system (centripetal force) acts towards the centre of the circle. However, if a vehicle should over turn it's going to overturn outwards rather then inwards (the direction of the resulting force). What force if any causes the outward overturn?
It is not a force that causes this. It is the centrifugal effect (sometimes mistakenly called a "centrifugal force").
Think of the passengers inside the car. They are moving along with the car straight ahead. Then suddenly, the car turns and is pulled inwards at the wheels by friction. The passengers still continue forwards, but the car now moves away underneath them.
Then the passengers feel that they are swung outwards in the car, towards the far window. But in reality, it is not them who are swung outwards, it is rather the car which is moving into them, because it is turning and moving away from them from underneath them.
This "swinging-outwards" feeling - which we can call a centrifugal effect - is not unique to human beings. It is of course also felt by any object inside the car, including the car itself. The inwards force is only acting at the wheels, so the upper part of the car feels swung outwards because it wants to just continue straight while the bottom part of the car wants to turn. If the lower part of the car and the wheels are pulled too quickly inwards (if you turn too sharply), then the upper part can't follow along. And then you see the car tilting outwards.
It might be better (in the car example) to think of things from an inertial frame.
You're behind a car moving at high speed. Suddenly the driver turns the wheel to the left. This pivots the wheels touching the road and generates a lot of sideways forces due to friction.
These forces are to the left as well. But, because they're from tire friction, they are also at the bottom of the vehicle. If the vehicle is tall enough, this force at the bottom creates sufficient torque to spin the vehicle clockwise from your view.
With this view, there is a real force (tire friction) that is rotating the vehicle.