I am confused. Did you use the fill flash here? Almost looks like it.
1) If you did not use a flash then using a flash would help. BUT ..
2) If you did use the flash, then setting the camera to A mode and selecting a smaller aperture would help. Depending on camera model, the flash will force the speed to be quite slow...typically 1/125 or 1/200. Now the camera's operating systems are reading the exposure on the girls and they are in the shade. Therefore a typical default setting in P mode would be f5.6 and maybe 1/125 second. Well the bright sky requires a fraction of the exposure and therefore is burned. You need less exposure on the sky. Sooooo ... if the camera was set at (say) f 11 and the default flash speed was 1/125 that may help. But you are limited. Using the "sunny 16" rule, the EV (exposure value) of that sky at ISO 200 would be close to the equivalent of f16 at about 1/200 or 1/250 second. But your flash
won't may not work at those speeds so, you could reduce the ISO to 100. But it is also possible that with the on-board flash at 1/160 and f16 the girls will be underexposed, i.e. too dark. So selecting a slower ISO may help as well. It is never perfect.
This is a perfect situation for a flash and no mater how complicated the above ramblings may see, try fill flash in this situation again. Should work for you. Start with the camera set in P mode and go from there.
The other option is to put the girls in the sun so they are reflecting the same levels of light as the sky. If the sky is not important then put the girls in open shade (as you have done) BUT this time select a background that is also in the shade. Bright open shade is often better on people than bright sun.