Live and learn!
Deep breaths. I know how you feel. btdt.
Disengage. Once you can detach and disengage he can dump that crazy on your doorstep (or in your inbox) but you don't have to pick it up!
I learned that I could not ask him anything (like with the bill). No matter how simply and innocuous it will turn into exactly what you experienced every time. When he tries to draw you into the give/take do not respond. If he asks you your thoughts - ignore. It is a trap anyway. If you feel you need to acknowledge that you received an email simply reply and delete out everything except the part that says he might not make it on Wed. and reply with "OK". Ignore the rest.
I learned the hard way that I had to completely disengage from visitation. Life became so so much easier and more peaceful for me and my kids. I emailed him a schedule set up by the courts. Yes that caused a firestorm of baiting emails but I ignored them all. I re-sent that email (without a word) every single time he said he didn't know what was what. I quit contacting him to verify arrangements, coordinate things, discuss times or transportation, accommodations - nothing. I just made no plans on his days (actually I made some at home family plans so I could distract my kids so they weren't staring out the window or calling him constantly when he didn't show). I did not make any of my own plans so if he came or not was not a hardship for me. If I needed something - I hired a babysitter. To this day (he is sober now) he still tries to get me to be involved in arranging his visitation (which consisted of 12 days this summer) and I refused. I don't even talk to him anymore - how the hell am I supposed to figure out which days he should take off work? It is nuts.
Sort of an unrelated tip - I created one large email that had every bit of information he would ever need related to the kids. (Was part of our court order that I share info). All contact info he'd ever need. School info. Babysitters, coaches, Doctors, dentists, orthodontists. I created a separate photobucket account and uploaded pictures in there from time to time (this was a big 'thing' he'd harp on) and this email included web address and passwords, School calendar links, we have a campus portal to check grades, name and contact info for the local newspaper, you can access medical info on line for the specialists my kids see so he has the password to that, and any other bit of info he would harp on. It was a huge thing he'd get crazy over - these tiny details about every school event or community activity. We have four kids. To provide a blow by blow of every tiny activity etc. would be a full time job and never make him happy anyway. He can call the school and ask about a grade just as easy as I can, he can look at the calendar himself, and with the email he has no excuse to say I'm not giving him info. He wants to go to an IEP - call the school. You want to go to an appointment - show up - the appointments are listed on line 3 months in advance. Call the doctor - you are a parent - they will talk to you. I'm not your personal secretary. Anytime he had a complaint or bitched about me not sharing - I'd simply resend that email without a word. I bet I sent it a hundred times but it only took 3 seconds it was so slick and easy to do and I was holding up my end 100%. FWIW it was not about the kids and him knowing what they were doing - it was about playing games with me. I doubt he's ever utilized one word, one link, one contact on that list.