I've had a number of cars over the years and have driven some of them with over 100,000 miles on several 2000+ mile round trips with very few issues. That include a 1996 ford Contour (drove till 9 years old and 180K), A 1998 Pontiac Grand Prix GTP (drove to 170K and 16 years old) and a 2001 Chevy Impala (drove to 150K and 18 years old). I'm very anal retentive with my cars so these were all very well maintained.
The 1998 Grand Prix left me stranded once while under warranty at 20K with a failed alternator and once at 100K with a seized idler pully (now I replace them on my cars at 70-80K as a preventative.) both within 150 miles of my home. The contour only ever left me stranded when I had a cooling hose burst at 120K within a few miles of home. Arguably I should have replaced that sooner but chose not to because they were a few hundred dollars to replace because of the design and since many on the forums were choosing not to replace them I decided to push it. The Impala had an issue on a road trip at 60K where the catalytic converter got clogged up and the car lost power. That was a known issue that was fixed by a dealership on the trip under warranty.
So two issues were warranty failures that could happen with a rental as well and two were because I missed a maintenance issue either knowingly or with the idler pully I learned something new about that. So providing that all maintenance is up to date (which you should be doing anyways) I would take that car on the trip without a second thought.
The 1998 Grand Prix left me stranded once while under warranty at 20K with a failed alternator and once at 100K with a seized idler pully (now I replace them on my cars at 70-80K as a preventative.) both within 150 miles of my home. The contour only ever left me stranded when I had a cooling hose burst at 120K within a few miles of home. Arguably I should have replaced that sooner but chose not to because they were a few hundred dollars to replace because of the design and since many on the forums were choosing not to replace them I decided to push it. The Impala had an issue on a road trip at 60K where the catalytic converter got clogged up and the car lost power. That was a known issue that was fixed by a dealership on the trip under warranty.
So two issues were warranty failures that could happen with a rental as well and two were because I missed a maintenance issue either knowingly or with the idler pully I learned something new about that. So providing that all maintenance is up to date (which you should be doing anyways) I would take that car on the trip without a second thought.