>stannis burns his own daughter alive
Honestly, this one doesn't seem too out of character, he had 2 options
1. Don't burn her, most of his troops will desert, starve or freeze; ruining any chance he has of a successful battle, not to mention that there's a good chance Shireen would die in this scenario.
2. Burn her, lose his wife and a fraction of his troops but save many more people.
Stannis was always a cold pragmatist, no matter how much he loved Shireen he knew that the only way to get his army out of the blizzard was to make a sacrifice to the Red God.