Transisition

Seeking advice about how to handle the transition from preschool to home.  Paige goes to school from 8:30-11:30am on Tuesday and Thursday.  When I pick her up the kids who attend all day are getting ready for nap.  Paige appears to be really hungry and tired when I pick her up.  I learned to take a snack for the car ride home, but she does not want to eat or nap once we get home.  It seems like we've missed the window for food and nap.  (I think I've expressed what a terrible eater she is anyway so I have a feeling she's really not eating snack at school and if breakfast goes bad before school, she has to be starving!)  Any advice on what what to do when I get home?  Have lunch already prepared to serve her immediately?  Take her straight to bed for nap?  Suggestions on how to wind down after so much stimulation so we can get in lunch and then nap?   Nap time for her is usually between 2 and 3pm.  Thanks!