Thank you to those who gave me ideas of how to fix the problem.
To those who merely suggested that I shouldn't have a puppy, I hope that you might go back and read the OP. I spend nearly every minute of the day training and teaching my puppy and my children. Taking 5 minutes to put the children in their rooms or put the puppy outside doesn't make me a bad parent or pet owner. It just makes me human. If you are telling me that you spend every second of every day watching your dogs like a hawk then I will call you a liar.
We made an informed decision about getting a puppy and chose a puppy for many reasons. One of which is that my son is scared of older and larger dogs. Seeing Ginger little and watching her grow will be a great experience for my son and it will ease him into a more comfortable state once she starts to get bigger.
I take Ginger to training classes weekly and diligently repeat her lessons throughout each and every day. I walk her at least once a day and provide her with a variety of toys.
When she climbed under the fence I was just taking a few minutes to do the dishes. I wasn't sitting on my butt at the computer or watching TV, I was caring for my family. If I'm a bad person for letting her play by herself for a few minutes while I took care of my family then fine. Next time I'll crate her.