What are my rights as a parent in a CPS Santa Clara County "informal supervision" case?

I would proceed very carefully if I were you, for the following reasons.

First, regardless of one parent's isolated blow-ups, under California Penal Code section 273a it is also against the law when someone "having the care or custody of any child...PERMITS the person or health of that child to be injured." Your post acknowledges that your wife has been getting physically abusive; the court might decide that you willfully permitted it.

Second, although the informal supervision is voluntary, under California Welfare and Institiutions Code section 301 a voluntary informal supervision agreement is offered in a "case in which a social worker, after investigation of an application for petition or other investigation he or she is authorized to make, determines that a child is within the jurisdiction of the juvenile court or will probably soon be within that jurisdiction." The voluntary informal supervision is offered "in lieu of filing a petition" under section 332, and "If the family has refused to cooperate with the services being provided, the social worker may file a petition with the juvenile court pursuant to Section 332." The section 332 petition is a petition to declare the children wards of the court. (This language is on the Santa Clara County Informal Supervision Agreement that you may have signed.)

Your post says you are ready to go to court. But if the way you get to court is by refusing to cooperate anymore, and CPS files the section 332 petition, you might find that the court hearing mainly focuses on whether or not your children should be made wards of the court, and not about the things you want to talk about. Before you stop cooperating you might want to talk with an attorney who is experienced in dealing with CPS in Santa Clara County, about the specific facts of your case.

DISCLAIMER
I am licensed to practice law in California. This information is not applicable to states other than California. This response is intended as general education, not legal advice to be relied upon. I do not know the specific facts of your situation; under certain facts this information may be incorrect or irrelevant. This communication does not create an attorney/ client relationship. The questioner is urged to seek a personal consultation with an attorney.