Hi there,
The daycare should do as you say and put your daughter to sleep when she is tired,but maybe there is just to much going on for her to go to sleep.
My DD is 2 and she goes to daycare 2 times a week she has big sleeps there but that night she goes to bed early and crashes cause she had a big day.Cause your girl is still little she will be so tired when she gets home,maybe a lie down on the couch for 10mins.
I give her and DS dinner at 5 every night, bath then DS goes to bed( hes 7mths) and DD stayes up ( quite time) and goes to bed at 7,she gets up at 6 next morning.
It works well for me,you just need to see what suits your family best