Your central nervous system is still reacting as though you're in the danger you were in when you were with him, ie when he used to wake you up at night to shout at you, and he texts you, your system reacts in the same way. This is really normal. Years and years on I still get activated when I get a text, although it's got much much less over time and I'm not compelled to reply immediately like I used to be, or try to make it fair, as it never will be.
Every time you get contact from him you are compelled to leap into action and defend yourself, to try to prove that you're not the "bad person/unfit mother" he's allegating that you are. You need to get to to a place where what he thinks of you is none of your concern. Truly. You won't be able to appeal to his reasonable side by being sweet and reasonable. He doesn't have one, and the rare occasions he is reasonable, it's just another way to manipulate you.
He is, and probably will continue to, use every excuse to keep his hooks into you. He likes it when you're on the end of a string and he can pull you around. Cut him off. You can decide if you're going to join in, or not. Do not communicate with him outside of the app, stick to the court order, turn your notifications off and have a set time to check for messages, respond to any message that needs an answer with "noted". Do not get dragged into "chats".
The energy that you're spending on wondering what he's up to, and trying to make him be more reasonable will be better spend on enabling yourself to disengage, therapy would be a good shout for this, and if you don't have the means there is loads of resource online on YouTube and podcasts. Draw a line, you're no longer at his beck and call, physically or energetically. Concentrate on being a good mum, and you'll do that better when you're not a distracted bag of nerves.