You don't HAVE to let it continue- but honestly? She's old, shes decrepit, shes gonna die soon anyway. And plus, i dont think giving her rides her and there is gonna mess up your car =P You could tell her no, or talk to your husband about it, but that would be kind of a d*ck move 2bh with you. Like i agree with you, but it still would appear pretty selfish, just letting you know.
Plus, its not like shes making you waste your TIME driving her, or asking to drive it HERSELF- shes asking your husband to do it. And considering you and your husband are supposed to become one ANYWAY once you are married... if your husband wants to do it, and it makes him happy, why not let him drive your car and drive her around now and then? lol
ON THE OTHER HAND: YES YOU SHOULD LET HIM KNOW IT BOTHERS YOU. husbands and wives ALWAYS need to communicate EVERY little qualm they have. EVERYTHING. That's the #1 thing i tell my girlfriends or just hookups! And i know its not anything like marriage, but believe me- they never wanna leave me! Bcuz not only am i a pretty cool dude but i try my best to work with them!
So yeah, LET HIM KNOW. I'm not saying you have to actually STOP HIM from taking the car (as that would be semi rude), BUT you DEFINITELY should tell him.
That way, he might have a chance of going "idc if you want me to still take the car! if it bothers you, im gonna stop anyway. so your happy." and then its a win win situation!