Thanks everyone for the warm welcome
I know it's all-too easy to be a "search engine psychologist", and I'm not a psychologist and obviously couldn't diagnose people I'd never met even if I was, but... there are many professional psychologists in my family (it's how my parents met!), and I do know a bit about personality disorders, so, based on Alice's behaviour on social media - and courts do take this very seriously in divorce/custody hearings - I would say she is displaying several signs of what could be a cluster B personality disorder - I would suggest BPD. This is disproportionately common in actresses/models (Amber Heard being a classic recent example), because BPD people have huge underlying insecurity and so chase professions where they are excessively admired.
One of the top symptoms of BPD is "fear of abandonment", and so, as and when it happens, they react as if it is the worst, most unendurable thing in the world - as to them, it feels like it is. Alice's reaction to the split is disproportionate and over-the-top, and this could certainly be an indicator of an underlying disorder, and her history suggests she has many of the other symptoms of BPD (impulsive, self-destructive behaviours; extreme emotional swings; explosive anger; alcohol abuse).
If I was Ioan, I would be strongly pushing for a clinical evaluation from a psychologist, because if she has that disorder, it will a) give him a much better framework in which to understand, and therefore deal with, her seemingly completely irrational behaviour as they move forward as co-parents, and b) help galvanise her getting the precise kind of help and support she needs, which will enable to be a much better parent (not that she is an irredeemably awful one now, but there are obviously areas of concern).
I don't believe it is incidental that Alice has no relationship with her father, as this speaks of a childhood which must have had periods of intense emotional trauma, which are a necessary prerequisite for BPD to develop. She probably feared abandonment by her father, and is projecting a lot of that onto Ioan / relationships with men in general. She seems to have picked men she believed would never leave her - Ioan because he was younger / less powerful, and Olivier because he was gay. That might sound counterintuitive at first, but an advantage to being with a gay man is that he is never going to leave you for another woman. It is not unheard of for gay men to marry women and to have quiet "arrangements", e.g., they can discreetly see men on the side, as long as they stay with the family. That might have been an appealing set-up to someone as fearful of abandonment as Alice.
In fact, Alice's reaction to Ioan's departure far more resembles that of a child being abandoned by its father, than one adult being left by another. Her outrage, unrestrained emotional outbursts, and untempered fury would be fairly appropriate reactions for a young child whose father had walked out and was refusing any contact. But in Alice's mind, that is what the marital dissolution is equivalent to, as what has struck me is how she seems completely unable to accept that people do actually have the right to leave marriages. Marriage is not an unbreakable bond in the way that parenthood is, hence why divorce exists and adultery is not illegal (whereas abandoning your child - at least financially - is).
Alice is trying to punish Ioan like a furious child might do to a father who has left her, because I think this is a deeply embedded and unresolved emotional conflict at the heart of her personality - something clearly went very wrong between her and her father, and now those same issues are being played out by her towards all men she gets involved with.
These are all issues that can be treated and resolved with intensive therapy, but they have to be acknowledged first. This means acknowledgement by Alice - that she has a psychological issue that needs treating - and by Ioan - that his ex-wife is not merely being difficult or obstructive, but that she's actually not psychologically well. She's not actively choosing to be irrational, but her emotional abilities are very limited and distorted by her personality disorder. That her behaviour is so obviously self-destructive, but that she can't see it at all, suggests there is a very significant emotional and perceptual distortion at the centre of her personality and how she sees the world
Personality disorders are difficult (though not impossible) to treat, because unlike other psychological issues - depression, say, or OCD - they are not a symptom that an otherwise healthy person is experiencing, but rather, the personality disorder IS the person. These disorders typically develop so early that there isn't a healthy underlying personality that's separate from the disorder, and so personality disordered individuals can be very resistant to treatment, as they fear treating what is wrong with them (which is their actual personality) will annihilate them.
Treating a personality disorder is possible though, and it involves teaching the person re-parenting techniques to apply to themselves to try and heal some very deeply embedded early damage, and then teaching them different behavioural skills - getting them to understand they need to behave differently in certain situations, even if they have strong feelings saying otherwise - and gradually moving them beyond the worst excesses of a personality disorder (and the good news is these do tend to burn out and be less all-consuming as people age).
As I say, cluster B disorders are very common amongst actresses / models and so it certainly isn't far-fetched to imagine Alice might have one. As Amber Heard was clinically evaluated as part of the trial, and she and Johnny didn't even have children to consider, I would imagine it would be eminently possible to arrange a clinical evaluation for Alice.
It might really help her to see why this split has hit her so hard and why she is dealing with it in such a self-destructive way: that being how she is is not her "fault" (she did not do this damage to herself) - but that fixing it is entirely her responsibility.