Here is the bottom line: if the city could establish that the "destruction" was to terrorize, threaten or exert control over their "victim" as an act of domestic violence the city would have strong case for Domestic Violence Criminal Mischief. It is not in the statute, but that seems to be implied based on what courts across the land have said when reviewing such cases. Here is how one New York court put it:

"[B]atterers often damage property to terrorize, threaten and exert control over victims of domestic violence." People v. Kheyfets, (N.Y. Sup. Ct. 1997).

In the above mentioned case, if his teenager was over the age of 18 and living at home, she would have a reasonable claim to the door on her room as property that she has a proprietary interest in. If dad, during an argument kicks the door in, I think you would have a strong argument that it was done with intent to threaten or exert control over the teenage daughter and therefore, officer could very easily charge him with Domestic Violence Criminal Mischief, and with other young children in the home that have the potential of seeing or hearing the incident occur, he would face an additional charge(s) of Domestic Violence In The Presence of a Child.