Focus on getting yourself home. There is no reason why CM can't issue an infant ticket even when the adult tickets are issued by UA. While you will have to pay for that ticket, it should not be a problem for UA to refund the infant ticket it issued.

Once you are home, then deal with the insurance issues. Given that CM told you that the infant ticket issue had been fixed, the problem is almost certainly on the CM side of the house. Yes, you were improperly denied boarding. But, good luck with that.

I would keep track of your direct trip interruption expenses and make a claim. Do not hold your breath.