This one was quite easy. Instead of taking that first right just keep going straight. Eventually it will adjust your route accordingly. Follow the route from there as normal. Just be mindful of traffic cars and you should easily get a 3 star time with little or no damage (if your skill at driving is better than mine that is)
Like with a lot of the Top Gear story, it isn't exactly faster to follow the exact route they give you. It wouldn't surprise me if the same holds with the rest of this latest Horizon Story.