Thanks @redshoeblueshoe and @ringonright hand.
@Picnicathangingrock - I got to thinking some more about this on the train this morning (your post got me reflecting on how the girls are doing at the moment, and whether there's more I need to be doing). And there's one thing I didn't touch on last night, that's pretty important (and a live issue for me, given some of their mum's behaviour at the moment). That's how you deal with them seeing poor behaviour from the other parent.
All of the divorce advice for supporting kids rightly says that you should avoid criticising the other parent to the kids. Very good advice, for obvious reasons. But I have learned that there are exceptions. My ex is very emotionally volatile (she has mental health issues), and sometimes she takes that out on the kids. They have also seen her behaving very aggressively towards me even after the divorce. Sometimes, the way she treats them makes no sense to them (because it's deeply irrational) and can upset them a lot. I have learned a few techniques for supporting them through that, and teaching them about what is and isn't appropriate.
In these cases, they need to hear that what they've experienced isn't okay and it isn't normal. We talk about what upset them, what might be causing that behaviour, and ways of dealing with it. But I am always careful to criticise the behaviour, not the person. And we talk about how they can handle it without accepting it - helping them to set boundaries.
One of the hardest conversations we ever had to have was after the assault, when my ex and her family spent a lot of time telling the girls how terrible it was that my parents had called the police. I had to walk a very fine line between being clear that violence is never acceptable from anyone, and not alienating them from their mum.
It's that line that is the hardest thing to walk, but which is so important. They have to feel validated and heard, and they need to know when things aren't acceptable, while still recognising the importance of their relationship with the other parent. It's not an easy one, but my advice is to not take never criticising the other parent to heart so strongly that it normalised things that aren't okay.