With limited exception, your Union should be your first active line of offense. Whenever your request for an FMLA absence is denied, consult with your Union Representatives/Stewards to initiate a grievance. With very few exceptions, I have found that Union Stewards are very dedicated, and more often than not, they will bend over backwards to help you. Always file a grievance. Courts will review whether you exhausted your "administrative remedies" and the grievance/arbitration process is an "administrative remedy".
Your Union is there to protect your rights and benefits, and the FMLA is a benefit entitlement given to you by Congress. The Agency does not have the right to break the rules, bend them their way to your detriment, or utilize loopholes in the law to deny, or otherwise disallow, your FMLA request. The law is the law, and no one person, or entity, is above it.
Unfortunately, even though you may win a grievance that is filed under the grievance/arbitration process, it is doubtful that it will be a precedent setting "win". For the most part, at least what I've seen, most grievances involving FMLA violations are settled without setting a precedent. Grievances that are settled at the arbitration level normally set a precedent.
Check out the Common FMLA Violations page
to see how the Agency violates the FMLA in other parts of the District. Whatever you intend on doing,
please file a grievance for any violations of the FMLA if the situation cannot be amiably (to wit, in good faith) worked out.
FMLA is a benefit of employment, and it is not a benefit that management
can give at their discretion, or take away without justifiable cause.