I am not exactly sure what standing you might think that you have to do anything in this case other than in relation to your own property. You have no standing to take any sort of action against the mother of your son's girlfriend. Even if someone did have standing, such as your son, there would be no legal basis for any action against this woman's mother.
This issue of the alleged domestic violence
is completely between your son and his girlfriend, and now the State, since he has been arrested. He can, if he chooses file charges against his girlfriend as well if she hit him too or first. Other than that he needs to speak to his criminal
defense attorney about the particular facts of his case to see if his attorney thinks he can get the charges dismissed or at least reduced to something like disturbing the peace, if anything.
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