I think my mum is racist to my mixed race daughter?

I’m Australian Caucasian (white) married to an Asian man. We have a 16mo daughter together. We speak a combination of English and Mandarin Chinese at home. I am also fluent in Korean so I try to speak that with our daughter when I can. The words our daughter does speak are about half English and half Chinese. She goes to a preschool one day a week where they only speak English.

We have a rule that if our daughter is watching TV (she very rarely does please no judgement here) it can’t be in English. She gets so much English at preschool and with almost all her friends, so we just want to benefit her by immersing her in other languages.

At Christmas time I was visiting my mother (3 hours drive away so we don’t see her that often) and she and I both wanted to do our makeup at the same time. My mum suggested I play some YouTube on her iPad for my daughter to keep her busy. I said I don’t like to use screens as babysitters, but my mum kinda pushed for it so I gave in, and started playing some Chinese Elmo. My mum immediately told me to turn it off. She said that she won’t have any non-English in her house. Her husband is even more intolerant than she is, and she said it’s lucky he didn’t hear it. This wasn’t a surprise to me. Before our daughter was even born my hubby and I were told off multiple times for speaking Chinese in their house, even if we were only talking to each other or saying that we love each other when passing by in the hallway. We eventually got used to only speaking English in their house, but it feels super restrictive.

Also, my mum keeps calling my daughter ‘bubby/babi’ as a loving pet name. (Like ‘bub’ it’s semi common to say this in Australia). In my husbands native language it’s a racist slur used to describe his race, literally meaning ‘pig’. I have asked my mum multiple times to please not use this term, but she keeps saying it. She told me that when my daughter is with AUSSIE grandma, she will do AUSSIE things. She even went so far as to say that we live in Australia, and more or less said that my daughter shouldn’t embrace any other culture.

My mum is actually such a loving grandma in every other way than this and has never made any comments about my daughter’s appearance etc. She basically doesn’t care that my daughter looks different, but wants her to act completely white bc she lives in Australia.

Would love any input on this, tips on how to have a conversation with my mum, similar experiences etc.