your girl is asian right? im an asian girl. i know lots of asian girls. i want to tell you that there are some similar traits between some of them. they (we!) can usually be very manipulative, ie mess with people's minds. it's the reason i'm not close with a lot of asian girls, lots of them are so cunning and just plain b*tches! i know scores and scores of asian girls personally who mess a lot of guys about. or at least chase them, lead them on then ditch them. its a common scenario that they have pressures from family and use a bf as a scapegoat and a release, sometimes they do it to be rebellious. no this is not generalising no this is not stereotyping blah blah blah, it's just what i see commonly among asian girls. steer clear from the mess she is dragging you into for no reason. have some dignity and say to her that you are not going to get involved in her messy business because really you don't have any responsibility to. tell her to sort it out. be her friend through it. it will take A LOT for her to stand up to her family because this probably means they will no longer accept her and they will make life difficult for her. it's already obvious she won't do it. therefore in my eyes the chances of her giving up her fiance for you are slim. the fact you have only been dating one month and its an LDR makes those chances even slimmer.
having said all that, it's very difficult to comment on an individual situation because it could be different from the way i'm perceiving it. i can only comment as far as my judgement of your posts allows me to. so i apologise in advance because in no way do i mean to say i am perfectly right. it's what i see commonly and therefore i am only assuming your case is similar to those.