Based on this if. It seems that what your ex is saying is that by having the kids on your insurance they no longer can be on the all kids plan.Now my ex is claiming that I must immediately cancel my plan because there are issues with the All Kids plan. She hasn't given me any real details other than her word that they are dropping the plan because of my insurance.
I would guess the reason mom is so mad is that most state run insurance don't have a copay for appointments and meds or its a very low copay such as a few dollar or such. Most non state run insurance have a larger copay for appointments and for meds it depends on the meds. Bet you mom dose not want to have to pay the higher cost copays.