It sounds like the father is begging to return to court. What a waste of resources! If you were married to the man, look at your divorce decree and/or parenting agreement. Usually providing an insurance card is mentioned. If you were not married, look at all your parenting papers for the same thing. Then go to a lawyer and discuss your options. Perhaps a demand letter would solve your problem. Good luck.
Just the threat of dragging him in to court should (but won't necessarily) make him provide the insurance card. Check your divorce papers (judgment of dissolution and/or parenting agreement) for the requirement of providing you with a card. If your court papers provide that both parents have insurance cards, you can either drag him to court or mediation. Again, just the threat of doing so may make him do the right thing.
Nothing in this post creates an attorney-client relationship. This post is not meant to serve as legal advice.