Should and how do I have a co parenting relationship with my ex husband ?

Also, without trips, clubs, anything wjth extra money, I don't ask at all. I explain to my kids about budgeting and managing money in very simple terms. If I can't afford it they can't do it. I will sell their old things, speak to school about a payment plan or any support they can give, benefits, things like that which I hate having to ask for help from strangers but I won't give ex the satisfaction as he will always say no. But he will also tell the kids things like mum needs to manage her money, I give her money, what is she spending it on? And that type of thjng.

Have a look at the Power and Control wheel. It is very interesting and helps me to understand his actions and how/why they affect me.

Similar situation here except both my kids are under 6. Ex does the same appearing when he wants.
I don't speak, I say hi and bye for the kids sake if he comes near me.
I now have a plan with the kids that if they are with me and ex attends, then they can go see him and I will wait. They can come over when they are ready. If they are on his time and I attend (award ceremony recently was the first occasion) I will say hi and bye, but they don't need to worry about me. Just have fun is what i tell them.
I stay well away, talk to the other parents, take a book or headphones depending on the situation (we have lots of hospital appts). I have now started to think ahead to situations where he could pop up and work out a plan for me, including the escape plan (he doesn't let them leave, takes their full attention and drags out goodbyes so the kids have started getting tears). So I wait patiently and have also before the event told them what we will do once we leave (park, film night, icecream, play cars) so they know that when we leave we have something fun to do. I do this as habit now because I never know when he will appear. It has helped massively.
Grey rock.
Parenting app is amazing for me as I turn off notifications when kids are with me. Everything in writing. You don't have to respond unless kid focused, and yiu don't have to read them immediately, every other day is fine and do it at say 8pm so you can deal wjth the messages and then distract with something so you don't overthink them all day.
Use chat gpt to make your response professional and not emotional.
Dad puts a show on and acts all friendly when girlfriend appeared at a handover recently. I ignored him besides hello and said hello to her And was warmer.
If you haven't already, therapy really helped me understand my physical and fight or flight reactions. Even just a message can give me physical reactions.
It is ridiculously hard. I'm 18months past our split, and I still get that horrible feeling. But working on having an alloted time to overthink/worry/panic and write down all of these thought and then time is up, move on to something i enjoy. It has helped and was something I learnt in therapy.

Keep going the way you did before the divorce OP. Don’t answer phone calls unless you think it’s an emergency. Contact via email only. I ‘parallel parent’ with my DC father and have done for 10years. We don’t speak, communicate via text/email only. If he’s at an event, I ignore and avoid. Sure, it’s not ideal, but in cases of past abuse and just having an inability to coparent, it’s the best option all around.

Watching your thread with interest as there will be good advice coming I think.
It feels like a life long punishment for a mother. If you chose (fell in his trap) the wrong man years ago to have children with, every person around you plus the courts seem to expect you "to do wat is best for your children". With which they mean you have to put all his abuse aside and be a kind and accomodating person to someone that has treated you like shit.
How?
I have no clue.