We get it. We comply and get little or no credit while the ex fights everything and gets few or weak consequences. It's almost as though the court sees us as more responsible and thus more consequence-worthy but keeps acting more as a passive referee hoping the players figure it out, as though you're only bickering.
In my experience the problem is that a psych eval is quite limited. My ex and I were both ordered to take psych evals when we initially separated. I complied. No surprise, the university grad student's report listed "anxiety". My ex? To this day, over 2 decades later, I don't even know whether she even took her psych eval. And yes, no consequences.
What I learned from that experience is that when you both are ordered to do something, might be a good idea for your attorney to merely inform the other side you've got your part done and wait for them to appear and submit their part. Otherwise you'll comply and be left whistling in the wind.
As CC43 wrote, a mental health diagnosis by itself will mean little, it's the impact of her parenting on the kids. In my case I had a few magistrates who were of no help but eventually the rotation came around to the no-nonsense magistrate. Between the magistrates, a lengthy Custody Evaluation by a respected expert child psychologist, a GAL for our child and my lawyer... the disparagement, the obstruction and the legal sabotage were addressed. Sadly, we didn't get to that point until long after my two year divorce.
That publicity posturing is somewhat rare here and we have to be careful not to speculate, but with your ex doing all this publicity amplifying all the issues, I wonder whether you might conclude she's co-morbid with Histrionic PD, where she must be the center of attention.
We had a member here over a decade ago who had an ex like that and that BPD/HPD combo was devastating and had their family court tied up in circles.
Are you still in the divorce process? Are you still living under a temp order? Do you have a Guardian ad Litem (GAL = lawyer representing the children)? As with a Custody Evaluator, a GAL must be well qualified, experienced, unbiased and not easily gullible. My divorce took 2 years, yet it took several more years before court finally addressed her antics. Once I obtained full legal guardianship (custody) and went back successfully to get majority time, my ex's entitlement balloon deflated a bit and we never went to court again. However, if your ex is Histrionic, whether diagnosed or not, even that may not resolve the conflict.
Divorce has been final. This is a custody modification. Coached the kids to make false outcries, once PD CPS and who knows what else got involved it was proven fake. Thankfully I know how to document and I have everything that shows the truth. So we are under temp orders that match our basic original decree. She plays a part, and once she wants to be this moral ethical amazing person that fights for the underdog that is who her part is in public and she gets all these supporters, even though she yells, screams, talks bad about me and all kinds of other terrible parenting. The issue is that she lies, twists, exaggerates the truth to be what she wants, then when confronted with actual evidence showing the truth instead of backing down it turns into well its a conspiracy theory, she said her former attorney, the judge, DA, CPS and everyone else is involved in this giant cover up with me. Then emergency filings saying kids are in danger. Over and over and over again. I'm just trying to figure out how this ends, sanctions? she never paid. Attorneys fees awarded? She never paid. This feels like legalized harassment and there has to be something that can be done to stop this.