S.M.
Looks like you are getting the same advice I would give, but let me tell you, I understand the mother in law situation! We actually had to tell a relative they were no longer allowed to take our 5 yr old places, as they decided her carseat was not necessary. Luckily, she was smart enough to tell us that "so and so" forgot her seat.
Please remember to do what is in the best interest of the child. Older generations just do not understand the carseat thing, but they are vital! Cars are made differently now, and the seats are designed to reflect that. There is a reason children should be in those seats until 4 foot 9. It's for their safety!