The law is reason, free from passion (Aristotle)
You have to follow the law where you live, not the cultural practice of your wife's childhood. Unfortunately you can't let the emotions of your wife, your mother-in-law, or even your daughter endanger your child or put you as the driver at risk with police. I'd recommend your wife watch road safety videos or take your daughter on an outing to the local police station to learn what police are, and how they help people. They will check that your car seat is installed correctly and they'll show your daughter how she should be seated. Maybe she'll take it more seriously if she hears it from friendly officers instead of her mum and grandmum.
Your daughter will need to follow the law in many situations as she grows up, whether she agrees with the law or not. I'm sure you'll want her to wear a seatbelt when she drives, and not drink and drive. You wouldn't want her to stay out all night, take drugs, or participate in any other activities which could jeopardise her wellbeing.
_________________
I never give you my number, I only give you my situation.
Beatles