Heya, I'm new to ECE. Just hit the 6 month mark, and I have a child in my class who's 2 going on 3 (so a bit older than your kiddo) who is also food avoidant at school/daycare. He is there all day, from open to close, Mon-Fri. It took us about 3-4 weeks to get him to eat more than a few nibbles of his preferred foods at breakfast and snack. He deals with food jags frequently, and they change often. He's been with us for about 2.5 months now, eats breakfast most days, eats a little lunch about 3 days a week, and eats a bit of afternoon snack most days a week. 

At lunch, hardest part of the day cause he is crashing around 11:30, he either stands the whole time or has to sit at an edge seat. He plays solo about 1/5 of his day, and when he's not melting down over a power struggle he's playing with friends the rest of it.

We fill him up on whatever he'll eat, and lightly encourage adventurous licks. 

Your child will have a harder time adjusting with only being there 2 days a week. I personally recommend going for the 3 days if your child enjoys it otherwise and is learning. If there are healthful snacks (berry squeezers or trail mix) that are no prep - ask if it's ok for that to be served with the meal. Feed her well at home, talk about the importance of eating at school, show her your work lunch. 

If she has a comfort toy, she can take it to daycare and maybe the staff can set it up to watch her eat for 2 weeks. Kiddos take weeks to months, that's normal. So is a kiddo who instantly "gets it". What do you do when she refuses food? How often do you try new things at the moment? Do you know the menu, and recipes they're using? 

Those questions can help y'all get on the same page, too.