DD (2.4) goes to MILs one day a fortnight. MIL has a nephew who is a month older than DD, and MIL looks after him on a different day.
MIL has a seat in her car for both children to use. Unfortunately MIL struggles with adjusting the straps so has just left them so they fit the bigger child which is MILs DN, but he's quite a lot bigger than DD - DD is very small for her age, only just weighs 9kg (22lb) and is in 12-18 clothes, the DN is in 3-4 clothes and must weigh at least 30lb (13kg). So DD slides around in the seat and can get herself out of it. I consider it both mine and MILs responsibility to ensure the child is kept safe in the car.
I don't drive but have a seat I use in my DMs car which I could borrow to put in MILs car for the time she has DD. The seat is adjusted to fit DD perfectly and she can't get out of it. MIL has borrowed the seat before when her DNs childminder was ill and his mum needed to work so MIL had both children on the one day.
So WIBU to ask MIL to use our carseat and explain the reasons why? I know if she had an accident and DD was seriously hurt or worse she'd never forgive herself. Would you be offended if asked to use a specific seat for your grandchild?