Physical & Emotional Abuse Support Group
Abuse is a general term for the treatment of someone that causes some kind of harm (to the abused person, to the abusers themselves, or to someone else) that is unlawful or wrongful. No one deserves abuse, period. Abuse can be emotional, physical, or sexual.
He proved to you that he hasn't changed. Just because you broke No Contact doesn't mean you can't go No Contact again. That's the good thing about No Contact. You can start it again and again. :-) If you block him, his friends, your mutual friends & his family from your phone, email, social media, etc., then you won't have to worry about what he is saying/doing. That will give you Total No Contact.
In addition, if you haven't already, please do Ilene's Clarifying Index Card Exercise.
http://www.dailystrength.org/c/Physical_Emotional_Abuse/forum/11590808-ilenes-clarifying-index-card-exercise
Then each time you're tempted to contact/respond to him, go thru the cards to remind you that he is an unchanged abuser who is not going to change and that his words do not match his actions.
If you won't do it for yourself, do it for your child. Children learn what they live and live what they learn. So s/he will grow up thinking its ok to abuse and be abused. Even if he doesn't abuse her, witnessing the abuse causes serious emotional damage. Remember children know way more than we give them credit for AND they sense things too. So please take good care of (and protect) you and your child.
~healing hugs~
Don't be mad at yourself for falling for his lies, if you want to be mad at someone be mad at him for doing this to you. And be proud of yourself for stopping it now rather than letting it drag on.
You are not back at square one, you never will be. You are seeing clearly, so chalk this one up to experience and know with certainty next time that he's a liar who will not change. And that you don't have to give him the benefit of any slight doubt there might be. What he has done to you is enough for you to be perfectly justified in saying "no 3rd chances".
He's not changed. You know what you need to do...
Hugs.