How to get adult daycare to cover caregiver working hours?

The adult daycare in Connecticut does not cover enough hours to allow working caregivers to drop off and pickup their family members outside of working hours. Where I currently live, in Texas, there is, in fact, an overlap of working hours (7 am - 6 pm), to allow caregivers to drop off and pickup their family members outside of working hours. I am contemplating a move to Connecticut for a job offer, and I am now wondering how to make this work. I just learned of the shorter hours of adult daycare in Connecticut.