I have been through this OP, I'm sorry to read this. I'm a very long time lurker...I have only been able to read and not reply for years, and this made me come back on.
I split from abusive EXH 10 years ago...and at that time things were quite different (iPhones not been about long etc).
If you type shared parenting into App Store search, they have quite a few apps that look good, I wish I had those. I don't however have experience of them, so I don't know how good they are. Obviously he has to use the app!My ex used to constantly change email addresses and phones and say he hadn't got my email, or reply by text and made it impossible to have a trail to work out what was happening. Or say something on the phone then deny it. I always confirm in writing anything like that.
I had some great advice from a charity and a psychologist (I had PTSD):
Don't respond to anything emotional. Just don't engage. Occasionally I would reply to a terrible accusation, but the result was awful and endless comms. Keep going back with the exact question, and a statement. For example:
"Ds1 has a dentist appt on Monday at 4pm when he is with you, please confirm if you can take him. If I don't hear by Friday I will cancel the appt." I would generally only arrange these things on my time with them, as my ex used to do this and leave me hanging.
Same for pick up/drop offs. Don't wait around if you are being mucked about. "We've agreed a pick up time of 6pm. Please collect DS1 at this time or we will not be there". This means you may end up with children but you need to establish an agreed time etc. I know all the games with lateness/sickness/work meetings/car breaking down. Be flexible to a point of course because those things happen to us all, but if it's every time, that's about control.
Maybe say to him by email "I'm very keen to make coparenting a success, and am not happy to use email/text/phone calls any longer, so I'm setting up a shared parenting app we can both use called xxx, which will make it easier to book appts and share information on a calendar of shared dates on our DCs. I believe it will make it easier for us both to put DC first and see what plans they have. I will set this up and share with your email address starting on 1 April, all arrangements and appointments will go on there and I will no longer reply to emails or texts on children arrangements as it has become unviable". Or something...?
The biggest thing for me was not engaging. It is so hard when you are being attacked. Keep going. Be firm, factual, not emotional, arrangements only.
My psychologist advised me to treat him like a 3 year old child with very very tight boundaries, and to withdraw any emotional involvement in conversations. If that starts state "I'm happy to talk about arrangements and issues relating to our DC. I'm not happy to discuss this any longer so I'm going to hang up now". It is very hard, but STAY CALM...it seems very cold, but I honestly find it helps to just stick to facts.
Also if he rehashes old emails (I remember this well) copy and paste your response one line. "I disrepute this and will not discuss further". IME he is playing a game, loves 'winning' and getting one over on you. Maybe just maybe, having a baby will take up more of his time?!
I think if he thinks he can needle you with this emotional abuse and it upsets you, then that's a form of power, because you aren't in a relationship now, this is all he has. It doesn't work overnight, but keep going ok? Message me anytime OP, this is a horrid situation