Should I take threats from a former professor seriously? Some Context:

A member of my MA thesis committee, for whom I was also a GA (graduate assistant), threatened me several times while I was still in my masters program (last year). For example, she threatened to fire me from my GA position with them-- which, in fact, she cannot do (only the department head can remove a GA from their position). When she realized she had no power to fire me, she threatened not to write me letters of rec for doctoral programs. She tried to pressure me into promoting her from reader to thesis chair on my thesis committee. I was very afraid of her at the time because she was my work supervisor, my professor (I was taking a class with her at the time), and a reader on my thesis committee.

I was afraid she would diminish my reputation in the department, give me a bad grade in her class, delay my graduation by holding up the thesis process, and not write me any letters of recommendation or worse, write me a bad letter of recommendation for a doctoral program. I did not stand up for myself or for others to whom she was abusive until I graduated last summer; I saw her retaliate against other students (primarily through grades and intradepartmental reputation) and I felt sure she could carry out some of her threats toward me. She bragged to me and other students that she successfully reduced the scholarly reputation of an academic at another institution whom she said was 'inauthentic.' Shortly before graduating, I did leave a record with the Ombuds of her treatment of me.

Now: I asked her to write a letter of rec for one of my PhD apps because I was afraid she'd be insulted if I didn't ask her for a single one (this is probably ridiculous, I know). I was accepted to that program and have decided to go there. However, this professor continues to be hostile toward me. In a recent email, she told me she had "just spoken to" the graduate adviser of the program I will attend in the fall, and implied that she speaks to this adviser regularly as if they are friends (somehow I think she's lying). Because of a pattern of behavior, I recognized that she still wants me to be afraid of her. I am loathe to admit that it's working, I think primarily out of ignorance of how academic/institutional relationships truly function (tempted to play the First Gen card here).

Question: Are such inter-institutional threats actionable, i.e. how likely is it that faculty at one institution can influence faculty at another institution in order to negatively affect the reputation of a student? 

Please note: The question is not, "Is this professor a bad person?" or anything to that effect.

If this question is too individualized, I will take it down. I feel like I can't be the only one who has experienced/is experiencing a situation like this. I would appreciate generalizable advice (e.g. across disciplines, types of academic relationships), especially from academics who have gone through similar situations.
This sounds terrible, and like you said, I definitely think asking her to write a letter of rec was a mistake.  However, regardless of whether she tried to sabotage you or not, you've been admitted!  Congratulations.

Now is the time to sever all contact with her and move on.

You left a record with your previous university about your issues with her, and if she was going to create problems at your new school I really think it would have come before you were admitted, especially since she was a letter writer.  Whatever she did or did not say, they gave you a big vote of confidence in offering you a place.  Time to focus on the next stage.

Good luck!