There are Federal laws that dictate when you are allowed to add or drop dependents from your employer-sponsored coverage. You can made the change during Open Enrollment every year but outside of that, there has to be an IRS-approved "qualified life event" before you can make any changes. It cannot be done any time you want. That's Federal law, not the employer being obstructive. Even with a qualified life event, there's only a short window in which to make the change. Usually 30 days.

"It didn't go through" can mean a lot of things. If you can find out more about WHY it didn't go through, I may be able to help more. But if not, if she really is stuck for now, a divorce would be a qualified life event and she'd have (probably) 30 days from the date the divorce is final on which to drop him.