SM and I divorced years ago. We have a child who is 6 years old and he received a dependent ID card. The SM cancelled his card once and, with legal help from the military installation where it was confiscated, the child received another ID. Recently the SM got him another ID and is refusing to release it. I cannot prove the child's health insurance illegibility and I was advised from ID office to go a different route because, even if they issue a 30 days card, the SM can keep on cancelling the card that is in our possession. I do not know what legal ways to pursue.
Dependent ID cards can be as confusing as anything else from DoD and VA. https://www.cac.mil/Portals/53/Documents/required_docs.pdf
I've been in and out of on base military ID offices over the years any number of times and they're always been helpful and on point. I needed some help from a local Navy installation late last year and was treated promptly and respectfully.
I think that's where you need to take this and then listen carefully to what they say.
If you think your ex isn't complying with the divorce decree, you'll have to return to the family court that has jurisdiction and let the judge sort it out. This is often the best solution.