I feel like there's a piece here where maybe the LW feels that because of his close connection to the family (and maybe because he "shower[s] her with birthday and Christmas gifts" and doesn't miss a game) he is entitled to a close connection with 13yo and her positive regard, which...no, and trying to force that because it's "how you treat people" is a really good way to teach her you don't respect her individuality, autonomy, and right to set boundaries and choose her own friends. Which would not endear the LW to me or to a lot of the folks I know, 13 or not.

Giving her space is a good start, but there's more that needs to happen to relate to her as a person and show one will respect her modes of engaging or not engaging.