First off if there is an emergency medical problem you need to be made aware of it immediately.....if your ex doesn't understand that or some Elder or other family member thinks they need to keep you out of it especially linking that decision to some vague JW concerns a letter from your attorney needs to be sent to all parties spelling out that you and your ex are the decision makers.
Let them all know this is a legal matter not a religious one.
Way ahead of you. After "the milk incident" in the convention i went and see a lawyer pronto. He written up a nice little letter and mailed it to my old congregation and even to Bethel. If my daughter goes to hospital for any reason in future, Elders and especially the HLC are not allowed to turn up without my explicit permission (which of coarse will never be given).
Also, check out my other thread of when my girlfriend asked me what JW's believe. She thought i was making it up as i went along. I said "no that's the GB".
https://www.jehovahs-witness.com/topic/5713659011530752/explaining-jw-beleifs-non-jws