I found the stubbornness of Alexandra's character somewhat maddening.
Yeah, I felt the same way. But thinking about it at the time, it did make sense, psychologically. And I am not sure that it was stubbornness in the end. Trying to reply without spoiling it for others, I hope:
after years of being pushed down and back from her immediate environment, the minute she was given an inch of freedom, she took a mile and ended up in the opposite end (also unhealthy and unrealistic) before she finally allowed herself to see that there was a middle way, and it was the one offering her the best opportunity for happiness and fulfillment as a woman and a human being. Edmund himself had to come out of his pre-made box also, and be brave enough to allow himself first to feel and then to show his own vulnerability so that she could see that it didn't have to be about the loss of freedom, but the gaining of something way more valuable and essential. OSIT.