If my DP receives a work call while we're eating out he will assess whether it can wait (ie if it's the boss or an important client he will answer it, if it's his colleagues it can wait!) then ask if I mind him answering it. He will then walk outside and talk there rather than loudly talking business in front of everyone in the restaurant. It's a bit annoying sitting alone for a bit, but no worse than if he popped to the loo most of the time and far preferable to sitting there twiddling my thumbs with him sat in front of me.
Examples of his ex's calls are wanting money for a holiday, wanting him to sort out some dressing up costume for a theme day at school, which only ever gets picked up at the last minute, telling him some family news from her side of the family, asking for passwords for the DCs to his iTunes etc. None of it is earth shattering, much of it could be sorted out by e.g. Her buying a costume and asking him to reimburse her (which he would) or texting for passwords etc.
She also insists on phone calls whenever we go on holiday (just me and him) to make sure he has landed safely etc. as she panics about him dying in an aeroplane crash (I'm pretty sure it would make the news if she needed to know!) She called him in the cab on our way home to the airport asking about our hol and asking if we'd had dodgy tummies. I really don't need her knowing about the state of my faeces!
Honestly, it's just too much and I agree with coconut about Kua, I'm sure my DP's ex thinks all is hunky dory with us all, as I wouldn't want to rock the boat by being anything other than friendly to her, but I really do wish she would butt out sometimes. There are times when I accept that she needs to be involved, but I don't need a third wheel in my relationship and frankly, it doesn't matter that she used to shag him, I would be aggrieved at anyone who constantly interrupted and inconvenienced my time with DP, whether it was a friend or other family member.
The only people who could rightly be forgiven for such intrusive behaviour are the DCs because a) they have a right to talk to their dad and b) they aren't yet old enough to understand about the niceties of social interaction and when it's appropriate. They will still butt in when he's talking to someone else in person, so obviously have trouble realising that interrupting is rude.
However, just like interrupting in person, kids will only learn that it is unacceptable if they are made to wait until you have finished speaking to be allowed their say. If they are always heard regardless of how rudely they butt in, they will grow up to be rude and to interupt people. Similarly their mum needs to be made to wait until an opportune moment to have her say. If it's an emergency then the opportune moment is right now, otherwise she can wait.