I'm not understanding you about discrepancies. As for the part about motives, I'm setting the record straight that I'm not communicating with this cousin to cause issues with exWW. We go back a long way.
When my kid told me what her mother said, I could have let it go, but I saw the possibility of exWW telling my kids that they aren't allowed to see their relative if they're with me, so it was an opportunity to nip that in the bud.
I did tell exWW that I'm not doing this to cause harm or upset her, that her relative treats everyone the same.
The final email is meant to ram home that I won't be disrespected by someone who can't keep any agreement (she broke several), would pick my kids up at times when it wasn't her turn to have custody of them and always without telling me. I could go on but you get the point.