Mirror-less camera question

I am in the process of identifying the best mirror-less camera to purchase for my wife and I am in need of some assistance.  She wants something that is a step up from a point and shoot, but she is not ready to go DSLR.  I have looked at the Sony Nex 5r, Nex 6, and the Olympus EPL5.  I am not sure which would be the best option based on her needs.  She will be using this mainly for taking pictures of my daughter, family photos, and our dogs.  She would want something that is not too big so she can put in her purse if necessary, able to take good pictures in low light settings, and would need to have a fast auto focus for moving objects.   I am not set on just these 3 if there is another model that would satisfy these needs.  Any assistance that is provided is greatly appreciated