He’s 14. He doesn’t need childcare. If you choose to have him on your own then it’s a favour to your DP, not his ex. She doesn’t get a say in what goes on in your home so just ignore that.
At his age, he can liaise with his dad direct and I very much doubt ex would “stop contact”, especially if she’s asking you to have him extra when she has plans.
As for the rest of it, your problem is with your DP as it’s up to him to maintain sensible boundaries. If he’s scared of her (can’t see why he would be but that’s how he feels) he’s not going to stop dancing to her tune and you can’t make him if he doesn’t want to or doesn’t feel able to.
Annoying, frustrating, aggravating - absolutely. But only he can change how he responds to her demands and it’s not going to change until DSS is an adult, so potentially another few years, and even then she’s not going to disappear.
I’d hunker down and accept things as they are if you really want to be with him. If it’s too stressful, there’s no shame is deciding it’s not for you.
Your DP needs his own relationship with the school. My DH gets everything by email or when he picks DSC up from school, letters and reports and goes to every parents evening, assembly etc. Then no reliance on ex to pass information on which would never happen.