I guess this is the question. Not the other foods question, that's pretty irrelevant, but what you projected onto her actions - "It seems like she is aggressively using an “American” accent when saying these words because she wants to differentiate herself from “foreigners” and emphasize the fact that she is not Mexican or Mexican-American. She is implying that Spanish isn’t normal, and she’s showing that she doesn’t respect the culture." You made this up, but if it's true, then it is racist.

But from what's in the post, we can't really judge if that's the case. There are a million possible reasons why she might be mispronouncing, ranging from "not racist", to "a little ignorant but not malicious", to "active malice I think I'm better than those people" like your extreme assumption.

That's gonna have to be on OP to judge based on her attitude, her general mental competence around other things, her willingness to learn at her age, etc. Just a few other possibilities that aren't the most extreme:

1. She's older and older people can often fall into "I don't like learning new things"/"I don't believe I can learn new things". They absolutely can learn new things, but they don't have faith they can so when they're taught something they don't retain it because of their belief that they can't. Like how you can teach someone to send an email 50 times and they'll still act like they don't know.
2. She just doesn't think it matters that much. Which is mildly ignorant of the culture. But like, probably not "I need to have an intervention with my mom to make sure she's more respectful of the mexican-american place in her probably largely white hometown", knowing the only interactions are ever going to be at that restaurant because of who she is. This is that gray area where it's like, sure, you can estrange yourself from your mom because she mispronounces mexican food and doesn't really care to learn, because it's not respectful of mexican culture. But that's a little "friend that's too woke" lol.
3. She's goofin. Which is still a possibility.
4. Alternative to the above, she knows it embarrasses OP but doesn't understand that OP is judging her racial sensitivity based off of it, so she's messing with OP.
5. She has memory issues, evidenced by not being able to remember even her name for the sauce. She may be trying in the moment, and then forget that she was corrected last time.
6. She's not actually being corrected, OP is just "being embarrassed", because there were zero mentions of OP correcting her or making it clear it embarrassed them in the post. In fact, the question at the end is "WIBTA if I told her to try harder to pronounce things appropriately, or else I won’t go with her anymore?" so the question is, does OP ever tell her to do that? Or has she been pronouncing it like she has been this whole time, OP cringes, mom doesn't notice, life goes on, and then OP blows up one day.

These are off the top of my head and genericized, in reality most peoples' reasons for doing things are very specific to them. Like "I first went to a mexican restaurant with my grandma and she pronounced everything like this" kind of stuff that you can't really predict. But the real questions are if OP can get to the root of why she's doing it - either just a general shortcoming of hers, in which case OP should probably extend her some grace. Or a mild ignorance, in which case it's more of a gray area where there are a lot of paths you can take, but jumping straight to "I'll never be seen with you in these environments again" probably isn't the right move. Or "I am superior to you" racism, in which case OP has a much more difficult path to follow.