I am the lead on a project that involves creating a procedure for a type of work and assigning it. The team I assign the work to has a different supervisor than I do. This sup and I do not have a good history in that she has undermined me and disrespected me both in my current role, which is a professional level, and my prior role, which was a step above people who do the actual work. She wasn't my sup then either, but I worked with her team at the time.
Here is a recap of our history:
In my prior position, I audited the quality of her team's work. There were two ways to access information and they should use the updated system because it was more accurate. However, the rule was, if they used the old system, and the information specific to the work item I audited was the same in both systems, no error was cited. Her team told her I cited errors for using the old system even when the information was the same. This was not true and I only found out about it months later from her in passing. She never came to me or my sup or researched it on her own, she validated her team and took them at their word. This was approx two years ago.
In my current position, which I've been in almost a year, she has let and encouraged someone on her team to gather data and create a presentation to show that the procedure I created was wrong. (It wasn't) This person had asked me questions and I addressed them correctly. This sup then asked the same questions, which I answered correctly. The sup had this person waste days of her time and I only found out about it from another person on her team. This happened a few months ago and I spoke to her about it.
She set up a meeting with me and two other people(who have the same job level as me, but also do not report to her and have nothing to do with this work) to discuss a procedure I created for a new type of work. On the invite, she included their sup, but not mine. That meeting got canceled and on the new invite, she included my sup(only because I asked her) but then also included her dept manager, but not mine.
After the second instance, I spoke with my sup and her manager and the sup in question has not talked to me since. How should I handle this now?