Those are good questions but all are open to innocuous answers. We don't know who initiated the initial meeting with any real clarity or even if there isn't always a meeting at that time of year or if the encounter being described was an official meeting.
Having to have someone to document what happens at a meeting with a coach because of her mental deterioration kind of supports nudging her out. I imagine that you meet with and talk to your coaches a lot and it is impractical to always have someone else present. Hart may not have even planned to broach the subject of retirement for all we know and it may have sprung organically from the conversation or Pat may have been the one to introduce the subject. I believe somewhere along the way it was stated that the purpose of the meeting was to discuss the logo.
On these first two points, I'll address from Summitt's affadavit. The meeting regarding the logo was initiated by Pat, who had heard that he was thinking about using the Power "T" for both men's and women's sports. It was not either of the two meetings in question, it was an earlier meeting again at Pat's request. So, we have Pat saying she initiated that meeting and it seems a logical conclusion that she didn't call the other meetings or she would have addressed that in the affadavit in the same manner. We also know the 1st( not the logo meeting) meeting was a "one on one" meeting, so we do know who was there, Hart and Summitt. You are right to say we don't know the purpose, but we do know that Pat came away with an impression and told "Jennings and others" what her impressions were.
If Hart did initiate everything then I guess the timing is an issue but it is his call when the program has had enough uncertainty. We may have been having trouble on the recruiting front or Pat may have been planning to meet with her advisers as soon as she got back and Hart wanted her to have his input or let her know that coming back as coach was not an option. It would be cruel to let her go through the motions of making a decision when the decision had already been made for her. We also don't know that there were no incidents that precipitated the timing. Out of respect to Pat I would not expect those to be aired publicly short of Jennings forcing it into the public by continuing to pursue her suit.
As to what prompted a second meeting we only have speculation. It could very easily have been something as simple as Hart realizing that Pat did not take the proper message away from the original conversation. In that case I don't see him having a beef with Jennings unless it was the way she went about things rather than what she did. For example she could have asked Hart what happened at the meeting and relayed what Pat had thought happened instead of assuming that Pat had the right of it from the start and yelling about lawsuits and violations.
We know the first meeting was at the beginning of the tournament, the second meeting sometime pretty soon after because she would be named Emeritus in less than a month I believe.
As for Jennings, all this hoopla is being generated because, Jennings believes that Hart(on this lone issue), is being retalitory and making Jennings out to be a liar. Pat's affadavit only says that the meeting Jennings refers to did in fact happen and that Pat told Jennings what Jennings reports Summitt said. Further, the affadvit addresses the logo issue and clearly Hart is caught dead to rights on that one. I don't think it's a big deal, but it was an error to tell Pat Summitt one thing and the media something different, and clearly Pat was angered by the fib.
Hart's response in the one e-mail we see from him seems to indicate that Jenning's should have known better than to say the things she said. That implies that he thought she had knowledge or should have had knowledge of things which contradicted what she was claiming. The e-mail I read from Jennings seemed to me to be an attempt to document her version of events. Whether that version comports with reality or not remains to be seen. I thought it was very clear that she was in fear of losing her job and she knew when she wrote the document that it would eventually be released for public consumption. It did not have the tenor or someone addressing their boss over issues from UT's perspective at all.