More than likely the girl was being removed from the home (under arrest) because the officer realized this situation could easily escalate between the mother and the child. I am going to guess that the girl probably hit her mother at some point during the altercation. We know she kicked the officer, that's one domestic assault and one assaulting a peace officer charge. Both of which have long lasting criminal repercussions in the US. They did her a favor by only charging her with disorderly conduct.
I can't say the tazing was justified, because I wasn't there, but if you have ever struggled with a truely pissed off 10 year old you may realize that they are not as easy to restrain as you would think.