The moment just before this is literally showing us that Black Lady wants to make Neo-Queen Serenity kneel to her, it’s very explicitly showing us that Black Lady wants to steal Mamoru away not because she wants to bone her dad, but because she’s jealous of her mother and wants to be elegant and graceful and mature like her, so she wants to have what her mother has.
They’ve made the explicit point that Chibi-Usa has felt like a third wheel between her parents before, that she’s spent the entire arc being terrified and feeling like she has no safe haven, except for Mamoru, who has been kind to her. Her relationship with Usagi is difficult, because she sees Usagi being kind and caring and having all this emotional support, she sees Usagi growing into the woman her Mama is, and she wants that for herself. She’s so envious, but she also feels like a burden to Usagi, she feels unwanted and left out in the cold from everyone.
Of course she wants to take the person that makes her feel safe and loved, of course she wants to take the person that is a symbol of her envy towards both Usagi and her mother. She’s a child twisted into an adult before she was ready and she desperately wants someone to hold onto, someone who loves her and makes her feel safe. With the way Wiseman manipulated her into turning against her mother and Sailor Moon of course she’s going to hang on with everything she has to the one person she feels she can trust, the one person who has always been kind and supportive to her, that she’s always been able to trust.