jetzzzzz>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.
Stannis sacrificing Shireen is almost definitely going to happen in the books given that GRR told Beinoff and Weiss certain major plot beats, from a thematic standpoint it works perfectly in concluding Stannis' character arc. The problem was always that especially in later seasons the time and space needed to build up to these events was never actually provided. That's why it really comes across as kinda confusing in the show