Can a parent ask the family court to order the other parent to cooperate with a CAS investigation?

Not directly. A family court's authority in a parenting case is over parenting time, decision-making responsibility, and support - it doesn't include the power to compel someone's cooperation with a children's aid society's own investigation, which proceeds under its own statutory authority separate from the family case. A family judge won't issue an order that essentially polices the CYFSA process.

What a family court can do is take a parent's refusal to cooperate with a society into account as a factor in deciding the parenting order itself, since the best-interests test looks at each parent's willingness and ability to protect the child. A judge can build protective terms into the parenting order in response to a genuine safety concern - for example, requiring supervised parenting time, restricting overnight stays, or setting other conditions - until the concern is resolved. If cooperation with the society is the real issue, the more direct route is usually to raise it within the protection proceeding itself, since that court and the society have the tools to address non-cooperation on their own timeline. A lawyer can help you decide which forum to use.