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.
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.