Can Dubai's visa be hacked to other cities in the UAE?

You can't go to other cities, because it is the UAE National Immigration Bureau, which is higher than the state/city and covers the whole country, but you can go to other countries, because your visa problem will only be filed with the UAE Immigration Bureau, and other countries will not show it unless you check your records specifically. However, if your passport is stamped with a special seal, other embassies will understand what it means at a glance, which will affect your visa application rate in other countries. You can keep your passport if you still have time.