Hey - I would like to offer my advice if I may.
Your OH Ex-wife sounds a lot like my OH's Ex-wife.
Here is how I cope. I say out of their arguments, I offer my OH support and listen to his rants about her and what she is doing. But I say out of it - I do not contact her. The other thing to do is to not encourage negative behaviour to continue. What I mean is that I let him get all the anger out in a safe place and then I start talking about positive steps that could be taken.
Its a very simple but it hard thing to keep up.
For example you have vented here - this is safe place no one is likely to get hurt or angry with what you said. But now lets draw a line under those feelings.
First things first; Communication (good and bad)
The ex wife overreaction to not being answered straight away - I would just ignore that. This is a call out for attention.
If your OH is worried about how his DD is feeling about the call - have a talk with her about it. Explain that you can not drive/bike and answer calls - it is dangerous for him and other road users. Say that as soon as it was safe your OH would have called back. You may find that she really is not that bothered but at least your OH has explained his side.
Both of you keep your feelings about her mother to yourself - if you can't say something nice then don't say nothing at all. The idea is that his DD has a nice area to go to - free from negative feelings.
It will also benefit you and your OH.
But if you really need to vent - then come back on here lady - that's what we are here for.
Ok the positive - you OH is involved with his DD and helps co parent the best way he can given the situation. His DD will know this and their relationship will only get stronger.
The after school clubs situation - its great that DD is active in all school areas. I am taking it that these are new clubs as the school year has just begun! Now could it be possible to ask DD to tell OH what her clubs are, what are the dates and times and does she need anything for them? Its another fun topic you could all talk about.
I hope I don't come across preachy, but doing things like this helped me and my ex husband work towards a good co parenting relationship.
We put the kids and their feelings first - any thing negative we keep away from the children
For a long time we just text information to each other as we could not bare to talk to one another.
My DD school helped us with our situation with their parent support group. They helped set up guild lines on how to behave.
At the end of the day, OP, the only thing we can really control are our words and our actions. Don't mind her hate filled words - just make sure that nothing can be thrown back at you.
You be a happier SM.