Is it ethical to reject part of your child's culture?

I thought this would be an interesting discussion. Me and my sister were just talking about how strange this situation is.

So my family is Dominican, and my cousin married a white woman that's American. They have a 2 year old together, but his wife doesn't allow their daughter to participate in anything related to our culture. For example, at the very few family events they attend (she doesn't like to attend them), she doesn't allow their daughter to eat any food our family makes. My aunt (the grandma of their daughter) babysits for them, and she's instructed to not feed her any rice, beans, plantains, pretty much any of our dishes. She wants their daughter to call my aunt grandma instead of abuela, even though spanish is my aunt's preferred language. She won't allow my cousin to teach their daughter spanish at all or even play spanish music around her, even if it's totally appropriate. She gave their daughter her last name bc she didn't want her to have a spanish last name. I don't know her reasoning, or why she married a Latino if she didn't want to accept any part of his culture. But I was wondering do you guys think it's ethical to completely reject a part of a child's heritage, especially when the parent that is part of that culture is present.

Thoughts?