Your daughter feels left out - and frankly, she is. How else do you expert a six-year old to feel? Maybe she would be better living full-time with Daddy - at least until you decide whether the "boyfriend" will be a family member or not. Right now, he is a guest in your home (and to your daughter, an uninvited and unwelcome guest). I think I would be upset, too.
This kind of situation would affect a young child 's emotions, ask your Boyfriend to play games with both of the girls its possible he is Favouring the younger one , younger children are easier to please, maybe a good thing to "spoil " her I dont think that hurts its nice to let children do and have exciting things, her Dad obviously does ,This is a matter of better Parent/child Interaction.When she says "you dont love me' she doesnt mean it , she feels left out as she sees you probably being loving with someone other than her Dad ,Divorce is very hard on children and it is a good thing that you and her Dad share her and her sister they need both of you in their lives.Cut her some slack, 'spoil'her and get your friend involved aswell.