I don’t understand the mediation bit though, she’ll never do it?!
Mediation can come in a lot of forms. There are some mediators who are quite collaborative, etc. But then there are other mediators, often former judges, who are good at giving parties the Come to Jesus lecture. They can, with their experience, pretty reliably tell a party what the outcome is likely to be and can strongarm a settlement. You put the parties in two separate rooms and the mediator jogs between them. The mediator can't tell each side what they told the opposing party so this can be a good chance for litigants to get an unvarnished look at their case. If the mediator is good and if that is their style.
Also, lots of courts require cases, especially family law cases, to go to mediation before they get set for trial. It is just part of the process of moving the case along. Mediation can also be a helpful way to narrow down the issues that need to be tried. The parties may actually agree on some points. Then, the mediator can report whether the mediation took place and whether the parties mediated in good faith (but no other details).
However, if AE jerks this around, walks out on the mediation, doesn't show up to a scheduled mediation, refuses to mediate, etc. then IG's attorneys can say, look we tried, set this fucker for trial. And the court will oblige. I used to do these pro bono and when parties balked at taking part, I filed my report and the case was set for trial.