I guess the poster will have to base her decision on her past dealings with her in-laws. If she's unsure, I would err on the side of protecting my child.
ILs drove nephew home w/o car seat - Page 2
Trajectory is the main reason for car seats, as kids are light weight and small and can be thrown from a car more easily than an adult, even on slight impact. I don't think anyone can argue that car seats haven't saved lives, especially even in low-impact situations. I weigh over 100 pounds and the chances of me being thrown from the car on sudden impact are far less than a light-weight object or living being. That's just science.
Good lordy, I remember driving with my dad and actually standing up in the front seat (in the middle) while he smoked cigarettes (this was in 1967). I love my dad, he was and is a good and loving person. But really, Dad? Wasn't there an ounce of common sense back then? And, he was in the sciences, so he should have known better. I'm alive because of pure luck.
Edited to add that the problem isn't always with one's own driving, but the driving of others. If anything, car seats should be seen as a defensive matter. I stress again that the older generation has a harder time with current requirements and protections, but the prime reason that these protections are now in place is because of the high fatality rate of previous times. I'm glad the laws are there. Driving is a privilege, not a right, IMO, and driving responsibly is even more important.
Kids so very rarely die in car accidents in Sweden, where rear facing until 4 + is common. Kids die in car accidents every single day in the US because they are not in a seat, the seat is not installed correctly or they are not in the right seat for them. Some accidents are not survivable but that is not the norm. The norm is that a kid in a correct harness installed correctly and used correctly to survive with little injury.
The question asked is akin to asking "Running across the freeway is deadly. Why would we even try to walk at all?"