I'm not hating on Jee at all. I like him more than Jun. Jun is certainly not my favourite, but she's growing on me.
As far as the promise on his deathbed goes... I think at the time she wanted to honor it. What is more important is Jun's happiness and if she wasn't happy, she did the right thing by leaving Jee. If she was miserable, ultimately Jee and his family would be miserable. She wouldn't be doing anyone any favours.
I see nothing wrong with breaking that promise.