Your ex sounds quite a lot like my ex-husband. Same behaviors, same insecurities, same reactions. But I realized early that responding in anger would only increase his anger. I was easily controlled because my mother had been utterly controlling, and as it turned out, I married what I knew. It took me 13 years to grow up enough to exit that marriage, 15 years to divorce him. How lucky for you that you never married this childish man.
There are a number of self-help processes that I personally found very empowering. One was reading I'm Okay, You're Okay, an older book that is still pretty popular today. It helped me stay in Adult mode when my husband lapsed into his Critical Parent mode. For awhile, that just made matters worse because he felt his power over me slipping, but eventually his rages became less frequent because they didn't have much visible effect on me. I found this book to be the single most important influence on my early adulthood.
Another, more contemporary assist is the wonderful website The Work (thework.org), which offers free materials so you can gradually change your relationship with your own thoughts, and consequently change your relationship with those people in your world who trouble you for any number of reasons.
If you can stop reacting to your ex and answering on his level, you'll give your daughter a new and better model to follow. She sees you feeling helpless and using anger to defend yourself, so she's coming to believe that only anger will empower her. She doesn't yet have the experience or imagination to see other possible responses or outcomes. Model them for her. Studies show that children are not negatively affected by their parents' fights IF the parents have a way to resolve those fights.
I agree that if you keep asking your ex to help you out with his daughter, his power over you will continue. You will probably do well to find other ways to meet those needs that don't lean on him.
Good luck. There is a better future waiting for you, if you are willing to take the steps you need to move yourself to a steadier, stronger, more adult foundation. Even if you didn't have that modeled for you in your own childhood, you can still learn it with some of the great resources available at your local library and online.