WA has very strict fraud laws when it comes to insurance. The state makes insurance companies put a specific fraud statement on all claim forms and applications. They have to say, "It is a crime to knowingly provide false, incomplete or misleading information to an insurance company for the purpose of defrauding the company. Penalties include imprisonment, fines and denial of insurance benefits."
In WA custody papers often contain a specific provision that copies of the insurance cards are to be provided to each parent. I would just send her a copy of the card front and back with a letter advising "Please be aware that it is a crime to knowingly provide false, incomplete or misleading information to an insurance company for the purpose of defrauding the company. Penalties include imprisonment, fines and denial of insurance benefits."
Worth a try. If you find out about fraud, I would definately report it to the insurance company. There is usually a phone number to report fraud on the insurance card or in the benefit book.