A few points:
- You wouldn't use the ablative like that without a preposition.
- aequor is a poetic word. mare is more often used in prose (or, as here, in more general usage).
- Since aequor (or whichever noun you do use) is dependent on Ardea, there is no reason why it would go into the plural.
- You would not put Ardea into the ablative plural after imperium, as far as I know.
As to what the correct form would be:
- I'm no expert in names, and I can't find an exact parallel, but I suspect an adjective (Ardea Maritima) would be more likely than the genitive (Ardea Maris)
- I've only seen imperium in the meaning 'X Empire' in the phrase imperium Rómánum, but I've never seen *Ardeánum (not to mention what to do with the adjective) so I would go with imperium Ardeae Maritimae.