No. I don’t think it’s gaslighting (twisting things to serve her own purposes). I do think that the two of you have some very significant problems in your relationship.
You each seem very reactive to the other. Your mother can’t handle your feelings. You can’t handle her comments. You each seem overly upset about what the other says/does/feels.
You are two adults who will inevitably have differences of opinion. It’s not a matter of figuring out who is right. In a healthy relationship, conflict gets worked out without so much emotional drama. For some reason, the two of you haven’t figured out how to approach a problem in a mutually supportive way.
I suggest you stop trying to analyze your mother’s feelings and actions and instead focus on your own. Please ask yourself why you are so emotional about what your mother says. (If your mother had written the letter, I’d be asking her something similar.) I can only guess that you may have some unresolved issues that are so close to the surface that it only takes a comment from your mom to put you into tears. Whatever the reason, it sounds very painful.
It would probably be helpful to see a therapist for some concrete suggestions and support in redefining the relationship between you and your mother. At some point, you and the therapist might invite your mother into some sessions to help the two of you move into an adult to adult relationship.
A healthy mother/daughter relationship can be one of the pleasures of life. I hope you and your mom will do the work to create a much more relaxed and supportive relationship with each other.
I wish you well.