We picked up a stray dog when he was about 5 months old (according to the vet). At the time, my kids were 2 and 3. It just so happens that my dog looks very much like a pit bull (though we've since learned that he is probably an american bull dog), but suffice to say, I was very nervous about this large, powerful animal that just kept on growing.
I was convinced after a few months, however, that he was the most docile, gentle dog on the planet. How did I come to this conclusion? Testing, testing and more testing. Under no circumstances was I going to be okay with this dog snapping at, biting, or even growling at my children. Not so much as curling a lip was acceptable. So (under close supervision, and after I had already tried it myself) I allowed my kids to take his bones/toys away from him, mess with his food while he was eating it, and even pull lightly on his tail and paws. All of the things that normally "trigger" aggression from dogs. I think he might have growled once, but quickly learned that wasn't acceptable when he got scolded for it. Since then (2 years later), my dog has proven time and again that he would NEVER hurt our kids. I caught my daughter pulling on his ear the other day, but all the poor animal did in response was cry. This giant 90 lb dog, crying at this tiny little girl for hurting him.
Teaching your kids to respect animals and not take things from them is important, but that's mainly for the times they encounter strange dogs. You have to expect more from your family dog, though. You have to assume that as long as you're all under the same roof, your kids WILL antagonize him in some way. You can't watch them every second of the day...it's just not realistic.
All that being said, you know your dog best. And it's possible that he sees your daughter as a "litter-mate", so to speak, and was only trying to put her in her place...not outright hurt her. But snapping at her face like that is truly concerning to me.
If you can find a good home for him, you might want to consider it. Or, you could simply observe him very closely for a while and see if he shows any signs of ever doing it again. I assume you got after him pretty well when he snapped at her, and that might have been enough. But you won't know for sure until you test his limits. So start taking toys away from him, messing with his food, pulling his tail etc. Then, while you're very close, have your daughter do the same things. And if you don't trust him enough to do this, you need to ask yourself why you own a dog that you can't trust.