Legal Question in Family Law in California

"a custody case that entails domestic violance" -What is the DV allegation exactly?

See the statute:

(a) The court shall refrain from making an order granting or modifying a custody order on an ex parte basis unless there has been a showing of immediate harm to the child or immediate risk that the child will be removed from the State of California.

(b) "Immediate harm to the child" includes, but is not limited to, the following:

(1) Having a parent who has committed acts of domestic violence, where the court determines that the acts of domestic violence are of recent origin or are a part of a demonstrated and continuing pattern of acts of domestic violence.

....

"children are being held indoors and the 6 year old is being withheld from school by him. Would that be considered an eligable reson to file for an ex parte?"

Notwithstanding domestic violence which is only alluded to; you can surely try and make your case, the issue would be up to the court. The judge has discretion to consider what is immediate harm and that will not be disturbed on appeal but for abuse of discretion. For instance you can surely try and make the case that the child is being harmed by not being in school and cite all the laws in your favor. But remember ex parte is extraordinary relief and in situations where visitation is being withheld a judge may continue it to a OSC hearing for the judge to clarify why visitation is being withheld and what is in the child's best interest.

"He is in violation of his court order"

You can file for contempt or seek a writ to return the child.