I could be wrong but having seen this play out in person, I believe this round is 'the show of force'. The lies, the tantrums, the sulks, the pretend amazing life etc have not gotten them what they want from the RF.
Since they returned to the UK it's clear they are just going to be royal (their version of royal) because dammit they are royal and no one is going to stop them. Every move from here on will be directed at showing the RF that they cannot be dismissed and they will be the most important members of the RF.
They are going to force it to happen by refusing to follow any of the rules laid out for them, and by continually pushing their narrative by showing up and doing things they are not suppose to be doing (all while shitting all over KC/W&C). It is going to be the worst shit show yet.
H wants W's role and M wants C's, and their DC are to replace W&C's DC (without the actual work). If they don't get it, M for sure will be happy to see the RF sink with H following her lead. It's going to get messy and costly very soon.
I don't think the school change is about them being dim about how things work, this is about them making a huge issue about everything good or bad - death by a thousand cuts for the RF.