Caregiver here but yes that has been a question parents have asked me and there are groups on both sides. I don't take kids out by car and many of the parents that choose me like that because they want their children where they left them so to speak and not out and about. Others don't choose me because they think their toddlers need trips to museums and far away places. To me those are the privilege of the parent to share with their child just as I did with my own and not my place but that is just me.

For sure I would make a decision on if you are going to use your car or not, get proper insurance and then let interviewing parents know that this a non negotiable part of your daycare and let them decide accordingly whether to choose you or not.