She is either a functional sociopath (meaning she minimally conforms to the the warped moral standards dictated by her religion in order to get by, but in reality has no cognizance of societal standards of right and wrong) or she has a severe case of moral compartimantilization in which she abides by one set of rules and standards in the real world and a different set when talking about her faith in the Bible. Trying to see the best in people I would hope for the latter but the end result is the same, a lack of rationality and critical thinking and self-righteous condonense of religious double standards.
I am inclined to go for the second view because I think many Christians do this. They compartmentalize different parts of the Bible based on what they think is important. The New Testament is generally heavily emphasized, with the Old Testament having much less weight, and large parts of the old testament never being mentioned(My church, for instance, while using a broad range of NT gospel readings, was very selective on the Old Testament, many of the stories such as these are never mentioned) and when I went to Catholic School, these sort of verses were ignored.
I think this is what Peg is doing. She is placing heaving emphasis on parts of the Bible which show God as merciful and just, and placing minimal importance on the parts that show God ordering the murder of children and condoning slavery and rape. Note that when she encounters an action not even she can justify(the murder of children even though she did try, she admitted she did not have an answer later on), she still refuses to admit it is wrong and instead decides there is some magical answer that would make it okay.
Peg: There isn't, as a perfect being, God is not just going to make a "good" choice, he would make the best possible choice. And the best possible choice would involve protecting the lives of innocent children.