I assume dad is now looking to file an initiating application for parenting orders and property settlement?
In parenting, I would seek what was agreed in the parenting plan as interim orders, and I would seek equal care as final orders.
It's true that a parenting plan isn't enforceable, but it still has quite some force in Court. It tells the judge what the parents have formally agreed is in the best interests of the children, and in interim hearings, that's the most persuasive evidence the Court can consider at the time.
In our case, dad had five nights a fortnight for two years after separation, and only agreed to three nights a fortnight in a parenting plan because it was better than the zero nights his ex had been facilitating for the preceding three months.
Yet that parenting plan became the interim orders anyway, because that was the only undisputed evidence available to the Court of what the parents had 'agreed' was best for their kid.
Now, the property matter crossover with parenting. Dad can't allude to the fact that mum's unilateral decision about care arrangements is attributed to property settlement because doing so is obviously speculative, and it's also irrelevant. He must focus on the reasons she has actually stated for withholding time, so he can remove those reasons for her.
The reason of a sleep disorder is creative, I'll admit, but also not very persuasive. I'm not a doctor, but I don't know that removing one parent is a common treatment method for a child's sleep disorder.
With that said, though, you know the drill - dad needs to assume this bogus diagnosis is truthful and ask mum and/or the lawyer for contact details of the doctor who diagnosed the kid so he can talk said doctor about the child's treatment plan and if there's anything he needs to do at his house to assist that treatment. Does the child need a special monitoring machine? Hire one. Does the child need medication? Get a scrip and pick some up. Does the child need to see a psychologist? Get a referral and tell mum you plan to book the child in. He needs to be 'on board' with the diagnosis until mum comes up with a new reason to withhold time.
Knock the reasons down one by one.
Re: property settlement, she's unlikely to get 70% of the assets. Even in cases where care of the kids constitutes a significant future need, the allowance up from a 50/50 split is maybe an extra 5% on average, and that can be quickly whittled away by financial contribution from before the marriage and by future needs like blindness. He's probably even positioned to seek 60% in his favour.