do/ have an about-face on sb/sth (to suddenly change course and go in the opposite direction; reverse one's opinion or course of action) — (полностью, радикально, кардинально) изменить курс; полностью передумать; изменить свой взгляд, отношение; сменить курс;
~ сменить гнев на милость (контекст)
do a flip-flop on sb/sth
do a one-eighty on sb/sth

Example 1: Mom thought it was a bad idea for me to marry Rick, but when he demonstrated how kind he was, she did an about-face on the subject.

Example 2: She did an about-face on her rule about not eating in the living room. Now we can do it if we want. (McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)

Example 3: We expected Dad to do a flip-flop concerning our vacation plans. (dictionary.reference.com)

Example 4: They had relied on Jim to vote for Harry, but he did a one-eighty and cast his vote for the incumbent (=an incumbent is someone who holds an official post at a particular time.) (dictionary.reference.com)

to flip-flop (on sth) {infml, disapproving}
If you say that someone, especially a politician, flip-flops on a decision, you are critical of them because they change their decision, so that they do or think the opposite.

...He has been criticized for flip-flopping on several key issues.
...He seemed so sure of his decision, how could he flip-flop so dramatically now?

an about-face (a sudden and complete change of someone's ideas, plans, or actions; a reversal of attitude or action) — поворот на 180 градусов; смена курса на 180 градусов

Related Vocabulary
[hairpin turn]
[change tune]
[change tack]