A. No. Irrational would be if you didn't flinch as your baby zooms off without you.
I suspect that you know it is only a matter of time before someone other than you or your husband acts as your child's driver, and you're willing to accept that somewhere down the road. The real problem is that your mother-in-law showed up for the job of chauffeur without even asking for an application. So now you either have to fire her (not an option) or explain your reservations with the hope that she won't take offense and that she will smilingly uninstall the car seat (not on your life).
Let's try door number three. First, make sure that your baby is as safe as possible. Tell your mother-in-law that you'd like to have her car seat checked by a professional to make sure it's installed properly. (Go to nhtsa.gov for free car-seat safety inspections in your area.) If she balks, trot out the statistic that more than 79 percent of car seats are used incorrectly.
Then ask to ride along on some errands (say you need to pick up a few things). Observe her driving skills. If all goes well, you'll have to admit to yourself that letting Grandma drive is okay. If all is not well, ask your husband to take a ride and see for himself. Then have him tell his own mother about your shared concerns, because coming from you, it might drive her away.