A visa is not required for US tourists to the UAE as long as your passport is valid for a minimum of six months after arrival, though a work visa on behalf of your wife would not be a bad thing.
Covid is still a pandemic there, you will have strict entry and exit plans to the nation, and will likely have to stay in an "airport hotel" for quarantine until you pass their restrictions. The apps and papers may not all line up for negative test results and vaccination records, if that happens, call the health numbers for assistance.
Shorts will likely get you "dress-coded" from almost any public location that you were not personally invited to come to. Slacks and a button-down shirt is welcomed. If a local tells you that you're not dressed enough, don't argue, just leave, or the police will be called. You will have to cover from your shoulders to below your knees. If you cover everything (you don't need to cover your face), then you are setting a better precedent for yourself.
Most places there will accept USD/CAD/Euro/GBP but you wont get good "personal exchange rates" and would be saving money by exchanging to the dirham (AED) at a bank or other official money exchange. Currently 1 USD ~ 3.5 AED.
Photos of people and government/military property without permission there is a huge issue and red flag, and can get you arrested, you don't want to be in trouble in the Middle East. If you want to do photography, do it in the mountains alone, or in places with permission and an accompanying guide. Their Customs may want to review any digital media before departing if you either claim large amounts or they search and find large amounts of SD cards, flash drives, hard drives, etc; or if you declare yourself as a photographer.
Pork and Alcohol is highly controlled, and will not be in markets, it is a Muslim country. You will have to find a "friend" for those, but the UAE sees even possession of alcohol similar to drugs, it comes with a risk. If you can go without drinking alcohol for the time there, that would be best.
Cigars are available, there are multiple LCDH in the UAE and other stores too. Airport Duty Frees will likely have the best prices in Dubai, along with UK Duty Free locations which you may pass through as a layover.
Driving is a must but don't drive yourself, get an "Uber" or hire a driver. You will get sun burns if you walk through the cities for long periods of time outdoors.
Sharjah and Ajman are run under Sharia law, if you decide to go there, it should be accompanied, and be prepared for strict observations.