I just watched a bit of this video, which appeared on YouTube next to the body language one. It's quite interesting to see an overview of the early part of their relationship and how things went wrong with the media, the public, and the other royals.
It mentions some of the text message exchanges and conversations between H&M and W&K which were reported in Spare (I haven't read it). Reading these, it's little wonder they fell out.
Kate sent a text to Meghan about the issue with Charlotte's dress and in response, Meghan imperiously tells Kate to take Charlotte to KP to have the dress adjusted "just like the other mothers."
She seems determined to put Kate and William in their place (she later tells William to "take his finger out of her face" when he points at her).
This is a recurrent motif. Either you believe in the hierarchy, in which case you behave respectfully to those who are above you in it - or you don't believe in it, in which case you don't present yourself using a title and you don't choose titles for your children.
It seems they want everyone to treat them as 'better' while treating their own 'betters' with contempt.