Passionate about a PhD in math, but unsure how to explain my chaotic transcript due to mental illness
You need to focus. Why do you think you need a PhD in mathematics? If you plan to be a serious researcher, how do you plan to balance that with working in your under-performing school district? What specific area of math is your intended focus? Are you trying to get into a top 5 program or any program? That also makes a difference. If you can show that you are focused today and have doable plans with a PhD, telling your story won't be as difficult as explaining a low grade in an entry-level math course such as differential calculus. You will have a hard time living that one down. Figure out why you earned a D and how that changed your approach to understanding math. You might want to consider applying to a MS mathematics program and state your intention to seek the PhD at that institution.