I think, like a lot of people (misguided, in my opinion), they decided to go their own ways but remain married for the sake of the children. People have done that forever, often to the absolute detriment of the kids.
Finally, as I understand it - (again from the news, I wasn’t there) - the Queen told them to divorce, and end all the strife and gossip.
And it’s pathetic that the Queen had to fix it all in the end.