Wow, how traumatizing for everyone! I completely understand your upset. Violence is not in His will and so, it is always shocking and traumatizing to those who DO follow His will.
So, what your husband has done is not acceptable and needs to be addressed. No question. Anger management counseling sounds appropriate.
Having said that, however, I also say this: He did not batter her, use a weapon on her or threaten her with one. It is not a repeated occurrence. (I assume from your post, anyway)
Being angry CAN be okay. And while your daughter will NEVER deserve violence against her, it is not okay to mouth off to your parent or to sass them and it is irritating to repeatedly ask for something which has already been deemed a “no”. Moping and sulking are incredibly irritating as well. If your husband has any other stressors as well, I can totally see why he would become angry with your daughter. Again, it’s never an excuse for violence, but your daughter was not innocent in this; she was not just sitting there and suddenly your husband grabbed her face, pushed her and called her names out of the blue. She needs to know that she is never at fault for violence, but I would say she had a part in the anger that preceeded it.
How you respond to this will be watched and internalized by your daughter. If you had forced her to go to the doctor or ER while connecting it with punishment for her father, it could be quite traumatizing. (BTW, having worked with kids and, indirectly with the police and DYFS for many years, a single incident that was scary but left few marks or lasting physical damages would be unlikely to result in punishment for your husband other than humiliation, which has inconsistent remediative success, but I digress). If she is dizzy, her pupils are dilated, she loses consciousness, sees spots or other disordered vision signs, or throws up, then the potential danger of a head injury would necessitate that trauma. But otherwise, basic first aid, comfort, and to be left alone by the offending parent at her discretion will be fine. If you believe that you or she are in immediate danger of being battered or killed, then you need to leave, regardless. However, if this is unusual behavior and your husband has both apologized and well as committed to change, then forcing her to live apart from him for more than the short term, could be more harmful to your daughter’s emotional health than staying and working it out. Calm, measured answers to her questions and assurances that the situation is past and handled, not ignored will help all of you to heal, if it’s possible for you. I am very emotional and it would be difficult for me not to just bolt or rage and I completely understand if that is what you want to do.
I hope this helps. It will take time and love and His grace to move on. But it sounds like you have all three. :hugs: