En castellano justamente se usa "doméstico" pero con un sustantivo que aclara de que se trata: "violencia doméstica".Hola Áristos,
Yes, in English, a domestic matter is a problem that arises within the home. In a general sense, it involves the rights and responsibilities of spouses, parents, children, and siblings and often includes child welfare, support, and custody. It can also refer to domestic abuse or violence. Essentially any dispute that arises within a family or home.
Does that help?