The answer is yes. There is nothing barring you from renting a car if you have a DUI on your record. However, rental companies have the right to refuse to rent a car to anyone with a DUI, and most of them do.
Before handing you the keys to a rental car, most companies are going to check your driving history. It is really a function of managing their risk. Most major companies will reject anyone who has a DUI on their record.
However, the time between your DUI conviction and when you request a rental also plays a factor in whether or not you will be denied. Different companies go back further than others. You may need to shop around or look at renting from one of the lesser companies. Because your options will be limited, it is best to do this before you travel.
Now, not all rental car companies check driving records. Therefore, they may not know about your DUI conviction. However, if you are not allowed to operate a vehicle for any reason, do not try to rent a car.
The answer to this is no. Car rental companies do not have rental cars with ignition interlock devices. The requirement that you drive with an interlock is specific to you, not the car you own. So if you have an interlock on your car at home, you cannot rent a car without one and drive it legally.
If you can’t rent a car, there are alternatives. Perhaps you can hire a private driver for your trip. Also, public transportation is usually an option. And ride-sharing services like Uber and Lyft may be a better alternative for your transportation needs.