H.G.
L., you definitely need to talk with your BF and explain if his daughter continues this behavior, she is NOT welcome in your home. this is not a joke, it is serious and going to negitively effect your own, sensitive, well behaved daughter. he needs to be a DAD... being a dad is fun AND discipline, or else his own little girl is going to grow up and continue to be a little antagonizing snot thinking its ok. it is not helping her, either by allowing this behavior....
if he allows it to continue, think of your child first and let him know that emotionally destroying your daughter is not tolerable and you can not marry into his family or be a part of his life... im sure the thought of losing you will make him do something to stop this, like put his kid in some serious behaviour counseling, and if not, then think of your little girl and say bye bye.