In an English-based discussion entirely around issues of race the ways racists commonly use the English language is very relevant. Using the word "momma" by itself is not offensive however in this context it is slightly offensive because the way you used it is exactly how a racist would use it to mock a black person.
I don't think people here are even taking a lot of offense at your use of the word so much as your extreme defensiveness over your use of it. Please take this opportunity to reflect on why you chose to be so defensive instead of taking a mea culpa (and, if you are genuinely confused by why people are offended, asking for clarification).
> So if a white writer would write such a book, they wouldn't be allowed to use the word "momma" or refer to anything that PoC might do that is different from white people?
This is, in fact, a complicated question. Generally the way to avoid being offensive in that situation is to write your characters respectfully as human beings first and foremost, to study portrayals written by members of the group you are portraying to see how they portray themselves, and to ask members of the minority group you are portraying to review your work for any unintentional offensiveness before publication.