One obvious option is the airport hotel in the terminal. The rooms are comfortable and amenities solid. It's not cheap, usually around AED 800 for a 24-hour stay.

Spending 18 hours in the terminal may not be your idea of fun (especially twice in a short period), but I kind of enjoy wandering around the airport, relaxing, enjoying the various shopping and F&B outlets and lounges, etc.

You could also check-in to the hotel and drop your luggage off in your room, then go backwards through transit security (this seems to work best in T1) and exit the airport at whatever point you wish. You could even try the hotel in T1 on one stay and in T3 on the next stay (I think that they even have or are planning a third branch in the new concourse -- not sure if that's open yet).