Instead of driving to Hatta, you should drive to Ras Al-Khaima. I usually do my visa run after midnight and it takes me about 90 mins to get there from the Dubai/Sharjah border. The good thing about the Ras Al-Khaima/Musandam(Oman) border is that you only have to walk for a minute to the Omani visa office, get your Omani entry-exit stamps and then walk back to the UAE border which takes another minute.

The whole process of leaving UAE, entering-exiting Oman, and then re-entering UAE takes me around 10 minutes.