I don't speak to my daughter's father. We have been divorced since June 2005 and stopped having any verbal communication during our divorce, sometime around October 2004. Initially we used lawyers to communicate (gets VERY expensive, but we didn't really have a choice - our verbal communication was SO unproductive, even the Judge at one point said he was not allowed in the courtroom during sessions, just his lawyer was present).
At this point we sort of alternate between text and email - depends on the issue. I ended up with sole custody and moved out of the state we were divorced in (a separate bag 'o worms) but since he is out of state we don't have much to deal with... she flies to see him twice a year so we have to communicate about that (which we do via text). I email him her school info (report card, progress reports - sometimes I scan assignments and send to him).
It was noted in our custody agreement how many days before he had to request in writing that he would exercise his visitation. If I didn't hear from him I text him so that all the times he doesn't take her it's on record that HE refused visitation. If he refused visitation I simply texted back "OK, let me know about spring break/christmas etc" and NOTHING ELSE. it's important to not engage. I wanted to say all sorts of things, but the fact that it was all written down made me hold my tongue - after all, if he cared what I thought we would still be together, right??? lol !
Note: When I lived in the same state we had some issues at drop off/pick up so we ended up with a mediator that was present at drop off/pick up so we didn't even see each other during the exchange. You can use someone official (which costs more) but then we switched so my SIL (his brother's wife) was the drop off/ pick up and he and I just communicated via text. Depending on your state you can set this up - she was actually named in our initial separation custody agreement as the drop off/pick up moderator.
One additional note - I'm not sure how old your daughter is, mine is now 9. However, right around 6 (when they go through a super-manipulative phase anyway) she sort of took this "well, you'll never know what I do at my dad's cuz ya'll don't talk" attitude. She even told her TEACHER (I was mortified). So, I enlisted the help of my SIL and during a couple visits I got a 'report' and then when she was home I slipped some of that info into the conversation and she flipped out and started asking "how do you know that?". I said "mommy ALWAYS knows what you do". She got over that phase pretty quickly. Anyway, if yours is young you might have that to contend with as well.
I would say it is definitely possible, as long as you don't bend to his manipulative ways. The more that you have in writing the less there is to communicate about anyway. Just stick to what is in your agreement.
It is a tricky situation - I felt alot like I was in a no-win, but once you just stop responding verbally and he sends a slew of bulls***t over email one letter from your lawyer will make him MUCH more cooperative. It's ugly, but it's probably better for your kid if you DON'T talk in cases where the talking is actually verbally insulting and screaming threats.
Hang in there!