I would not take a small car. SUV would be the best choice, if the price is ok. You will feel more secure. You will definately need insurance. I would take liability, theft and damage of glass. Insurance in case of un- insured or under-insured driver is a must! I'm not sure if you can have the insurance only for a part of the trip. The cost of the insurance could be approx. 1/4 of the total. Research online for a good deal.
Most car rental companies won't allow you to take the car into Mexico. But if you are only going to Mexico for few hours, you can park your car in the duty free store parking areas or any public parking sites before the border and cross the border using your passport for identification. Then either take the taxi to your destination or via several buses for your alternative mode of transportation. But you must have a little knowledge of Spanish for communication to enquire about directions. We experience to take a bus to their terminal in Rosario just for sightseeing along the way and little walk close to said terminal for at least 30 minutes and back to the border. We were lucky for not encountering any unpleasant incident but we met pleasant and friendly Mexicans during this daring this short es. Not recommended for not so brave travellers especially for lengthy driving in Mexico. Maybe long stay in resorts or driving with a licensed Mexican tour guide is highly recommendable.
They will not allow you to take their cars across the border. I asked last month when I rented from them
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