Xtina, I know that is a tough call. I have a 12 year old border collie mix I adopted from the pound that is snappy with toddlers. (Yes that is her in my avatar). I don't have any kids in my house, and I keep her away from children. She thinks that she knows what children should or should not be doing, and she believes that she can correct kids, just as if they were puppies. We have not been able to convince her otherwise - so she has no contact with children. If I had a child living at home, I would have to make the tough decision. If your dog is only snappy with kids, I would say that she could live out a happy and healthy life with a no-child household, and you should contact the shelter where you got her - making a full disclosure of the problem.
On the other hand, my good friend had a fear-aggressive dog that bit multiple people. She tried training which did not work, and ultimately had to make the right decision to put the dog down. He was a rescue who should never have been adopted out. It was heart-rending for her because to her, (and me) he was gentle and sweet. But he was completely unpredictable with other people. She had the choice of caging him 24 hours a day, or euthanizing him. Putting an aggressive dog outside where he can have contact with other people is not the right answer. She still misses that dog - but she made the mature and correct decision. Sadly, some of these guys have either had such a bad start, or have a genetic predisposition to fear aggression that they cannot be safe pets.
You have to be sure your child, and the public at large is safe.
I feel for you, because it would be so hard for me to part with my girl - even if I knew it was the 100% right thing to do.