I'm not going to allow my ex to be part of our daughter's life
Why would you do that to your ex? Do you think it's fair to your daughter?
My ex broke up with me when I gave birth to our daughter, so she doesn't deserve to be in our life.
This all seems like in the end it will only punish the child. You should think about your daughter and what she needs more than worry about your feelings, no matter how valid those feelings may be. You need to do what is right and let your child have access to whoever she needs.
By not letting my ex to be part of our child's life it will protect her from being abandoned that way again. That's what should happen. I am looking out for her as a parent.
I can understand your desire to protect her. What if your ex has changed and is trying to be better, though? Doesn't your daughter deserve the chance to know her?