I'm sorry I don't know anything about AD taxis, but if they operate the same as dubai taxis, they will be able to bring you back to Dubai. However, they then have to do the drive back to AD without a fare as they are not allowed to pick up clients outside of their own emirate, so I suspect this would be reflected in the cost, which is why it might be cheaper to hire a Dubai taxi for both legs of the journey.
Could you not just do a half day hire of a dubai taxi? Not sure how much it is now, but you get a driver assigned to you for 6 hours (I think its 6) so no problem with not being able to find him for the return journey. You arrange this through the normal taxi call centre.
Akhil 055 324 5088.
Akhil drives a clean and tidy luxury sedan, is a safe and reliable driver and speaks excellent English.
He does cost a little more than a standard taxi but for the sake of cleanliness and safety the small difference is worth it.
Tell him Tracy from Australia recommended him :)