Hi lowselfesteem92. Welcome to Psych Central. Sorry you are feeling not loved by bfs daughter
There are multiple issues that could be at play. Kids have 2 parents growing up and even after divorce or death these two people are imprinted in their minds. When someone else tries to take the place of one of their parents it can be rough going. Teen years are the worse. Sometimes ages 1-9 the child can be more grateful for having a parent but I felt a shift in the 10-13 year old stage. There was more distance.
Another factor is the daughter often has a fantasy of being dad's favorite. You as the girlfriend are competition. It is a tough place to be in. If it is just symbolic things like the cup, not taking it serious seems fine. If they start to get abusive verbally or otherwise I would talk to bf and see how they feel. If they do not take it seriously, then it could be an uphill battle.
Another way to cope is to cherish the memories of that closeness you once had and be patient until the daughter grows up and possibly outgrows these tendencies. Sometimes the teens find out that being an adult is not as easy as they thought and they need someone they confide in. If you have kept a respectable distance and not seemed like a threat to them, that person might be you.
These may be of interest
The Psychological Impact of Divorce on Adult Children
4 Tips for Helping Children With Abandonment Issues
Parenting after Traumatic Events: Ways to Support Children