since when did father's and mother's draw such a thin line as to obtaining something so valuable as insurance for their kids?
OP, regardless of what has happened in the past, I'm surprised you wouldn't continue WANTING to provide your daughter insurance via a private plan. From my stand point, she will always be your daughter and if you are financially capable to pay for ANY insurance, why not get it for her? Especially knowing your ex wife has tendencies to cancel policies and continue to collect your $ and squander it on things not of necessity. Add on another important factor: your daughter has a serious medical condition. I'm just a bit shocked that because of disputes between you and your ex-wife your daughter has to end up w/ no coverage over something as trivial as she's not going to be living w/ me anymore, she's 18 and you're tired of mother's games.
Be the bigger person and pay the last year remaining per the court order. You cannot foresee what happens in the future and as other posters have warned, you may end up w/ a bigger headache in the event she does need emergency medical treatment and you are responsible for 50% of the bill. Although the mother may be getting away w/ lots of things, don't play into the game. If you do, you're just like her. Do the right thing even if you don't think its right. In the end you will be on top.
Best of luck.