At first glance I think you are correct. If this is the case, and the D.A. accepts the charges you have a good argument for why it shouldn't apply. There is an argument to be made however, Section 71.003 defines "family" as 'parents of the same child, regardless of marriage,' and in that same section allows the definition from Tex. Gov't Code 573.004 which extends it further to relatives. They could always change the charge to Assault, also. I suggest talking to a local attorney for a more thorough answer. Good luck.
I agree with the previous answer that you should contact an attorney to determine your best course of action. Any time violence is involved, you should always seek help to make sure no one else is hurt any further.
Please consult a Criminal Defense attorney in your local area. Many attorneys, like myself, give a free initial consult and can give you clearer guidance based on all the specific facts of your case. Take all documentation with you for review by any attorney you contact, you will get a better assessment of your possible options and outcomes.
This answer is general information which does not establish any attorney-client relationship between the person asking a question and the person answering, or a duty to respond to ongoing questions; nor is it intended to replace competent legal assistance in the jurisdiction where the matter/issue arises or is before a Court.