Re: don't want to eat after daycare
My 4 yr old dd goes to an in-home daycare Mon, Wed & Fri where they have breakfast, lunch, snack & dinner if they are still there for it. Some nights she's not hungry to eat dinner with us b/c she's already eaten there... but she still sits with us anyway & picks a little at the food, totally understandable. Then there are other days when she eats dinner with us just fine.
If you are still concerned, you should talk to the daycare each day when you pick her up to find out exactly what she ate & around what time... if need be, ask them to write it down for you with the time. They should understand & want to help you out with this. If this is done & you are seeing what time she's eating & what she's getting to eat & still think there is a problem, talk to her ped.