If you still want an AIB card, send the form direct to AIB credit card centre. This will avoid any delays due to internal post from the branch.
You can't go the Ombudsman until you've exhausted the internal complaints procedures. Not sure what your best bet is for that. I've given up complaining (to any of the banks) on minor annoyances like this. Your complaint is just as likely to be mislaid as your original form was, and you'll just end up wasting more of your time!