If I have followed this correctly, I'm not sure about that refusal. If you applied for a LDC for a proposed revised design; it can be considered based upon the proposed drawings. If they show a PD dormer they should be granted.
What has been built is separate matter which the Council can pursue through through enforcement action, granting a LDC for a proposed dormer would not change that. You would at least have a potential solution by altering what has been built to make it PD. I can give some general advice but I'll do it on Darluc's post..