You are not your mom (or your dad, for that matter) thank goodness! So you can stop worrying about becoming either one of them. If you don't feel like contacting your dad right now, don't do it. Either he'll contact you or you will contact him when you're in a better headspace. He's not gonna change at this age so you just need to figure out how best to manage him. And what you're managing now is not giving him an opportunity to welch on his deal. So delaying communication may be a good strategy for now.
I do recommend you track your daughter's moods for a month - I wouldn't be surprised if you see a pattern.
Sounds like you're keeping good boundaries with her. I used to say my kids thought I was really stupid when they were teens until they were about 23, then all of a sudden mom was a genius again!
You might be right, that she's imitating things heard in her father's house. Or she may just be going through some moody teen drama. Don't take it personally.