I don't blame you for telling your daughter the truth. It's one thing if he had been a model ex - it's another thing when he's putting all the blame onto you for things you have nothing to do with! That's not a situation in which you need to lie, in my book. You put as positive a spin on it as you could.
There's something I've never told my kids about their father, and never likely will. I know it would worsen their impression of him. And frankly, it's something that happened early in the marriage before they were born. But man, I was mad when here I've kept that secret all these years out of respect for his relationship with them, and then find out he's said apparently despicable things to the kids about me. (I still don't know all of what was said, but son's girlfriend at the time was so offended that she felt she needed to leap into the fray and defend me, and son hasn't spoken to his father in the year and a half since.)
The good news is, as they grow up, they figure it out. Just stick to the high road (again, I AGREE with you telling her the truth when she asked, just don't give any more info than is required.)
Glad everything else is going well for you, sorry your ex is still a pill. It gets easier when the kids grow up and you have less reason for any contact.