In many cases, the right hamstring is trapped against the car seat while driving. This impedes circulation and recovery. You notice it more when training.

I've had better success moving the seat forward so the angle brought my knee up higher. I've tried adding a layer of stuff to the floor to get the hamstring up off the seat even more, but you want to avoid cluttering up the pedals. I tried driving with the other foot, which I still do, but I don't recommend it because it won't match your panic reactions in an emergency stop. Gives me temporary relief though, as does cruise control (a godsend), and massaging the hammies at stop lights.

Angled roads can be a factor, but it sounds like you have addressed that. If you are way out in the country, it could be the driving. Maybe there is a way to bolster the seat (or any chair for that matter) to optimize circulation in your hamstrings during the downtime. We only spend a certain amount of the day training, and the rest in recovery, which is why circulation then is so important.

Try a hamstring compression sleeve or wrap...that will assist with support and circulation.  It is not unusual that the problem is only on one side, there could well be other overall imbalances and contributing factors, as others have suggested.  Running on uneven surfaces is always risky, even for shorter distances.  In the future, you may want to be evaluated for custom orthos, and see a good sports PT, but I would say right away go with the quality compression product..it will most likely make a big difference and certainly should reduce the discomfort. 

They taught us about the wallet phenomenon, dubbed "back pocket sciatica," in school, but the hamstring problem described can afflict anyone who drives, wallet or not. I haven't worn one in many years. There is not only continual compression of the right hamstrings while working the pedals, but continual tension in the hamstrings as they are lightly flexed to keep the foot stable on the pedals. You wouldn't be able to work those pedals without this hamstring flexion. An excess of tonus in a muscle is a prescription for muscle fatigue and poor recovery, since the majority of healing takes place in the resting state.

This brings to mind a basic principle about healing and recovery that extends to the sport of running as well as our recovery from it. It is well known that running boosts immune system activity in general, but there is the paradox of the marathon, after which many experience a drop in immune system activity for a few days after the event.

I'm sure this change occurs during the event, just as digestion and other autonomic functions slow to spare energy for the running muscles. There is only so much energy and resource to go around, and extreme exercise poses a dilemma for the human body, which has to make tradeoffs to survive extreme sport.

One reason why rest is so important to athletes is this tendency to divert energy from one place to another based on need and availability. I'm not talking about metaphysical energy, but the metabolic and catabolic activities that are mustered by the body for different purposes at different times. Training athletes are known to require more sleep than the sedentary because this expenditure must be accounted for.

One reason why I emphasize relaxation of muscle tissue is to allow the healing process of immune system activity to take over in the absence of flexion, shortening recovery times. As a general rule, the more relaxed one's muscles are, the deeper one's sleep becomes. The benefits of rest are well known, as are the risks of chronic tension. Driving is just another example of how modern life can contribute to chronic tension, and in addition to neck, shoulder and back pain, right hamstring tension is a case in point.

The problem in this case, as Damien has suggested in numerous posts, is posed by the concept of the chair and how we tend to sit on it. There are numerous cultures in the world in which the chair is an unfamiliar object. It is no surprise that the elderly in such cultures often maintain erect posture into old age.

Here, we do everything in seats, from work to entertainment to extreme sports like spinning, cycling and car racing. In various seated positions we shorten or stretch our hamstrings as well as cut off their circulation, we shorten our hip flexors and draw the pelvis forward, adding an unhealthy curve to the spine, and tiring upper back and shoulder muscles, which must then arc forward to achieve balance.

It is easy to spot someone who spends too much time in chairs by how they walk. When people become too weak to stand, guess what? We put them in chairs. Of course, that's better than bed rest, the last stop before death for many. Aren't we glad we're active? But, am I sitting right now? You betcha. It's about the only comfortable way to use a computer! At least my butt is parked on the edge of a massage table with my legs straight, lol.;)

I understand what JamesJohnsonLMT says about compressing the hamstrings but I've found a higher driving position has helped me.