How should I go about publishing a manuscript in which my mentor does not actively support my best interests? I am at a loss of what to do. I had started working on this project, a systematic review and meta-analysis back in undergrad. I was a senior. Long story short, for a while my manuscript was going well. Come August 2016, my mentor stopped communicating with me in the final stages. Weeks of no responses predominated, and as a result I emailed the Chair of the department on 3 separate occasions (over a total of 7 months). I was promised 3 different deadlines, all of which went unfulfilled. I finally emailed the dean in April when we got close to my final deadline of May 1, 2017. I got my edits, but I was 3 days away from leaving the area because I was heading off to graduate school. 

I ended up telling my mentor I didn't want to publish or take this situation into a new institution, but if I found someone who could advise and help me with the situation I would reach out to her. I expressed I had felt we had failed to meet the deadline and the outlook was bleak. She responded positively saying we hadn't missed the deadline, but if I were open to forfeiting my primary authorship stance then she'd be glad to completely finish the manuscript. I took this as a direct offense to the work I had done because I had decided on the topic, done the data extraction, results, conclusions, and limitations of the paper.  

I have found someone but am worried my old mentor will not follow through or will hinder the process again. My new adviser suggested I send her an ultimatum and deadline for her final comments for the manuscript and submit to a journal. However, as I am not a researcher, am going to grad school to be a clinician (current graduation 2019), and only have a bachelor's degree, I am scared if I do this then I may lose her support for the manuscript.

How should I proceed?
First, regardless of what you do, secure your independence of her in every way: funding, reference letters, etc.  All that has to run smoothly without her.

Second, forget her.  Don't count on her finishing. She won't do that at all or if she does it, it won't happen personally, but she hires another student.

Third, prepare a journal submission, and get someone senior to read your paper and provide critical comments.  You need a more-or-less constant eye on the paper from some senior person in the area to guide you away from pitfalls you don't see due to the lack of experience.  If you don't have that person, count on a rejection of your first submission.

Fourth, put your prior, no longer supportive advisor either into acknowledgements or as the last coauthor, depending on how much of her contribution is left by the time point of submission. Submit the paper.