Yes, there USED to be an air shuttle between Dubai and Abu Dhabi. It used 2 Cessna Grand Caravan turboprops converted as seaplanes. Today you can see those planes taking tourists on joyrides over Dubai.
The original service flew from the Dubai Golf and Yacht Club on the creek to the Corniche in Abu Dhabi and back. It cost AED 350 one way and took nearly 2 hours to get there. Unfortunately the operator who set it up failed to consider the detours he must make on the way because of restricted airspace around royal properties on the coast.
When you could drive there in 1 hour for less than AED 50, who wanted to fly? They went bust after about 3 months and the aircraft were parked up for about 2 years until Seawings bought them and started operating their tours. They are now based at Umm Al Quwain Aeroclub.
Knight