Pit bulls and pit bull crosses have dominant personalities. Hitting her will have far less effect than hitting a whippet or most other breeds (it would take years to recover). That's in your favour. Pitties, like rottweiler's are hardy and cope well with strict discipline.
In many ways it's a natural response to grab the dog and chastise it. Grabbing her by the scruff of the neck and showing your aggression is not a bad thing. I'm not endorsing hitting, but not sure it's necessarily bad for such a potentially head strong breed in an extreme circumstance. Biting a child is an extreme circumstance. It depends on how hard you hit her. The aim is to show a clear sign of disapproval rather than harm the dog.
She needs to know it's not on and she will be jumped on. That's how dogs communicate when there's a serious infraction. They understand the emotional of the owner being angry and if the reaction is instant to the cause of the behaviour the dog will link it to the event of biting the child.
If she's being her normal self with you, it doesn't sound like there's much, if any, harm done to your relationship. Definitely making a habit of hitting a dog on the face will cause it to fear you and cringe.
It's never the dog's fault if they bite a child, it's the adult's responsibility. Dog's should not be left alone with small children.
The dog cannot be trusted with any children again. She must not be set up to fail. By that I mean put in a situation where she has to tolerate small children. She doesn't enjoy it. She may be unsure of the child, her status and she hasn't done it in malice. Animals are pure in their motives, she did what she thought she was supposed to do. She was communicating with the child in dog language. Acceptable family situation? Definitely not.
Your priority is to you child's safety first, followed by pet ownership. You clearly love your dog. Keep them separated.
We had a rottweiler when our children were young. He grew up with our eldest and loved and protected him. The next two he didn't like so much and would growl when he heard their baby noises. He viewed them as some small animal (I'm guessing). He was also getting older and probably had aches and pains from being a large breed.
So I kept them separated. The younger children were never allowed in the same space as the dog. There was always a gate, a fence or a door between them.
Finally he snapped at my toddler, luckily there was a gate between them. He was a 55 kg dog and he was getting older for a large breed. I had to make the difficult and heart wrenching decision to have him put to sleep.
I couldn't in good conscience rehome him, as there's a responsibility to other children that he may meet. The vet concurred. He could have killed my son. It was the hardest and saddest decision of my life. I still grieve it many years later. I remind myself, it would have been a far harder grief if he had bitten off my sons face or killed him.
