The oldest daughter 16 shaming me for the youngest girl 13 being my favorite

I have a 16SD and 13SD. I have been in their lives for almost 4 years. From the start the youngest took to me and the oldest shunned me. When I very first met them their aunt told me the youngest would most likely attach to me quickly because her mother clearly favored the oldest. I honestly thought she was being dramatic and put no thought past that to to it. Well come to find out their mom absolutely favors the oldest. She constantly does things for the oldest that she doesn’t for the youngest such as shopping trips and cruises for her birthday. Like she literally took the oldest and her three best friends on a cruise for her birthday and then gave the youngest $100 for her birthday and they are only a couple weeks apart. Like there is clearly a disparity there and I could name many other events just like this. Their mom hates me and the kids let me know she talks badly about very regularly. Now 4 years in and I am so close with the 14 year old. She like a little mini best friend of mine. We love to be together and spend a lot of time together. The SD16 makes it pretty obvious that she doesn’t like me and has even said that a few times to my face. It’s never really bother me. I get it, it’s a lot for a teenage girl to accept a new woman coming into her home. But this is where I am having an issue. She is harping on her dad that I am a terrible person because I do things for her sister and not her. I was adamant that isn’t true. Her sister and I have a friendly really and no I don’t with her but there isn’t anything I wild do for her sister that I would not do for her. So then she told her dad that we all three go to Starbucks and I buy her sisters but make her pay for her own. This has NEVER happened. I always buy for both girls. Then today I checked SD13 out from school early because she wasn’t feeling good. Her sister saw our location and asked why she was out of school with me and she said she got checked out. SD16 then replied of course she checked you out because she doesn’t like me. I was floored. The ironic thing is I have checked SD16 out of school 3 times this year at her request. This is the first time ever in the 4 years I have known them that SD13 has asked for me to get her. What makes SD16 have this poor me, she hates me attitude? Honestly it pushing me to stop doing anything for her and keep doing it for her sister if she wants to make me out to be that way. She is not a little kid, she’s 16 and she knows what she’s doing. She straight up lied about the Starbucks to make me look bad. I am having a hard time keep telling myself she’s just a kid and don’t let it get to you.