You found it rushed, I didn't. I expected it. I didn't find it out of character, I found it to be a consistent plot line waiting for a catalyst. From her earliest days as the alpha sibling under the surface, to her consistently destroying all her perceived enemies and anyone else in her path. Remember her satisfaction with her brother's death. I firmly believe, you and other members of the audience wanted a kinder caring Dany, as she purported herself to be, missing the undercurrent of who she really was, a monster. Whether she burnt the Dothraki leaders who opposed her or murdered all those she saw as betrayers and any who stood with them, she was always a member of her family of monsters. She has always seen herself as an all powerful goddess, with powers of destruction, absent creation. A vengeful goddess demanding sacrifices. Two of her children dead, her most caring personal follower decapitated, what else would you expect? Forgiveness? Burn, burn, burn baby was her motto and m.o. She was unleashed and unhinged to fulfill her destiny. The fire bearer. Her face after Milasandre's beheading said it all. The straw that broke the camel's back.
Jon and Tyrion, along with Jormah, functioned as her counterpoints, but they all failed. She is what she is. Deliverer of death, madness incarnate. Sansa saw through the facade.