The courts prefer parents to sort things out between them, but SIOs for school admissions do happen. In this case, if they had gone with the father's preferred order (which was originally agreed by the mother), it seems likely that the child would have got a place at the first preference on sibling priority.
If the mother wasn't happy with the agreed order, she should have applied to the courts for an SIO. That is what the courts expect parents to do regardless of any allegations of bullying and manipulation (for which you have no evidence and which are, in any case, irrelevant since what matters is the child's best interests).
The father had no opportunity to apply for an SIO himself. The parents agreed the order of preferences so, since the courts operate on a no order principle, he could not have got an SIO at that stage. When the father discovered that the mother had changed the order it was after January 15th, so there was nothing effective the court could do about it. They could order the mother to change the order back again, but there would be no guarantee that the LA would accept the change.
They both have PR. That means both opinions carry equal weight. However much you say otherwise, they do have to agree on the establishment and the order of preference. If they cannot agree, they must get an SIO. When both parents have PR, there are no circumstances in which it is acceptable for one parent to impose their view regarding school preferences on the other. That is the law. The courts have been very clear on the subject.
The mother's preference, whatever it was based on, is not a reason to usurp the father's choice of school.
You are projecting and inventing facts to suit your narrative.
The LA may be at fault. That is not manipulation. They clearly state that preferences cannot be changed after January 15th unless there is a good reason. Simply changing your mind is not a good reason. If that is the reason the LA allowed the mother to change the preferences, they got it wrong and their decision should be overturned by an appeal panel.
I suspect your posts would be very different if the father had changed the order of preferences without the mother's consent.