MIL calls baby "daughter of my heart/life/soul"

I don't know if this is the right place, but I'm frustrated and want to vent and see if I'm just being crazy. My (26F) MIL insists on calling my baby (9 months) "hijta de mi alma, hitja de mi Vida, hijta de mi corazon." When I was freshly post partum it bothered me so much. I told my fiance (26M) he needed to talk to her because it was making me angry, making me feel inferior as my babys mom, I didn't want anyone else touching her or holding her, including him, because I felt more protective and defensive because she was MY daughter and not his mom's. He tried talking to his mom and explaining to her she needed to stop. Her response was that she's a latina and passionate and can't help it, plus she shared her dad, his grandpa, with him and allowed him to call his grandpa Papi, so now he shares his daughter with her. Fiance held firm and she stopped for maybe 2 weeks, then it started again. I did have PPD/PPA, so I let it go thinking I was crazy and making a big deal out of nothing. Recently it's started bothering me again and I'm having the same feelings. I tried talking with her and telling her we're not doing nicknames anymore for the time being so baby starts to learn and respond to her name. She agreed but said in her heart the baby will always be "mi hijta." I guess I'm wondering if this is just a culture thing I need to accept and get used to, or if this is weird and overboard. Fiance thinks it's weird as well but brushes it off as his mom doesn't listen and it is what it is.

ETA: Since the replies are mixed, I want to clarify that if it's something that is common in the Hispanic culture, I will learn to accept it for what it is. Obviously this specific term of endearment is not something that's common to me and probably why it's so off-putting as a literal translation. Obviously I have work to due regarding PPD/PPA still, but I was really just wondering if this is something that I'm blowing out of proportion and letting under my skin too much. MIL and I had a good relationship prior to baby, we'd do lunch, shopping days, and see shows togther, so I'd hate for something like this to ruin our relationship, but I do feel like boundaries have to be respected. Also, the babies dad is very involved and hands on with her. I've never kept him from helping take care of her in any way. I expressed my feelings early PP that I was feeling like keeping baby away from everyone but knew that was irrational.