if you are experiencing gender based visibility issues in 3rd person, most likely the cause is your nif file. open the nif for the female model of your cloak and double check the bsdismemberment node (and also double check that the mesh is pointing to the correct one for female in your armor addon record)
likewise if the invisible mesh is for specific race (like argonian hood etc), open that particular race mesh nif and double check the node
Many thanks for the reply, AD. I'll look into these .nif issues.