Rental Cars in Puerto Rico

Make sure your credit card insurance, if you're using it, does not exclude Puerto Rico. No personal experience.

Tim is right - your primary issue will be to sort out the matter of the insurance.
It's been a while, but as I recall the drive from San Juan to Rincon is pretty straightforward. Road conditions are generally good and it's a divided highway most of the way. You can preview the drive yourself by using the Street View feature on Google maps.

Thanks for these suggestions. I understand the need for documentation of insurance. My MAIN CONCERN is the local rental car situation in San Juan. We are planning a Holiday trip, a little late, and the usual companies we use- Alamo, etc.- don't have much left, and they are very expensive. The local companies- Popular, Charley- have erratic reviews, so reliability is a major concern. Any suggestions are welcome, this being our first trip to PR, but knowledge of how well regarded these companies are is our top priority. Again, thanks for weighing in.

Was waiting for someone more knowledgeable and with more current experience to chime in on your behalf, but failing that I can only offer some general comments.
Out of curiosity I looked at the reviews for both Charley and Popular rental cars in San Juan. Though there's the usual smattering of negative reviews (usually from people with an axe to grind about the insurance cover) the bulk of the ratings seem to be generally positive for each, so I'd probably suggest proceeding with a booking - preferably with a company with a liberal cancellation policy so you can use that booking as a placeholder while you continue to research a better deal between now and your holiday travel date.
The holidays are going to be an expensive time to visit no matter how you cut it. Given the high cost of rental cars you might try to minimize the time you actually need one, maybe by relying on Uber or another ride share to get to Rincon and relying on public transportation from there or maybe just shortening your time in Rincon in favor of a few days in San Juan where you won't need a car. There's plenty to see and do in and around San Juan to keep you busy for several days.
I see too that there are a few local rental outlets near Rincon. You may have better luck researching one of those but, being local, be aware they may have restrictive opening hours.
Good luck.

Thanks so much for your thoughts. Great advice. I feel a little more at ease with the local rentals and I'll report back after the trip with my experience.