Daycare lunch is at 11.30, and by 5 pm pickup she's starving and cranky

Our toddler goes to daycare five days a week. They do lunch at 11.30, a nap, then a small snack around 3. By the time my partner collects her at 5 she's frantic, eats whatever is left in the bag in two minutes, and then won't touch dinner at 7.30. I asked if the snack could be bigger and they said all the children get the same. Is it fine to send something extra for the ride home, or does that just move the problem to dinner? My aai says feed her when she's hungry and stop watching the clock, which I suspect is right, but then dinner turns into a battle I lose every night.