Girlfriends kid

My (25) girlfriend(28) has a daughter who is 6 that I’m Having trouble with. I’ve only been around her daughter for about 2 months now. Despite all my attempts I’m having trouble getting her to like me. I have helped make a fort and bought the trolls movie, I play at the playground with her and the other kids and watch as they ride their bikes, we’ve gone to get ice cream, we have played games and went on walks. Normally she is fine and then out of nowhere she like wants me to leave. The other day she told her mom she wanted me to come over and play and I did since she asked and then she just took toys out of my hands, didn’t want me to play, kicked my leg(not that hard), and just kept sticking her tongue out when I tried to talk to her. We sat down and had a talk with her to try and get answers and at first she said she was jealous. I told her I wasn’t trying to take her mom away and she said yes you are. And that I don’t come there to visit her. She then later went on to say her dad doesn’t like me and has said some things. Today her dad called her mom and asked if I was being mean to her. And then also said that she told him that I drew a picture of myself sticking my tongue out at her and put it on her door. Mind you I have never been in or near her room and don’t go near that part of her place. My girlfriend told him that was all false and then asked him if he said anything and it said he hasn’t. So we are starting to get different stories and seems like she is just making stuff up. Her mom has always been the one to take care of her and kinda babies her. Her dad just recently started seeing someone with 2 kids of her own back in December. I’m wondering if this is just too much. All too soon and she’s just scared of losing her mom who she has always had or what’s happening. The fact that she is beginning to lie scares me and hurts me. Being a male dating a female with a young daughter who is lying makes me worry about what she could make up. Granted I never put myself in a situation where that could possibly be true but just the thought is scary to me. This is my first time dating someone with a kid. I’m not sure what to do or how to handle the situation. I try to do things with her and talk to her but it’s not working. Any advice would be appreciated. Thank you.