I think you need to look at the schedule a little closer.
I work full-time and dd (3.5y/o) goes to daycare. Girl gets up around 7:30 (on her own) every day. They have breakfast at 9 (I give her a snack on our drive in). They have lunch at 11:30. They nap from 12-2pm. Snack around 3:30. I pick her up just after 5 and give her a little snack on our drive home. Dinner is usually ready between 6-6:30 (although we have eaten as late as 7 or 7:30).
So, looking at your question, I don't see why she can't have lunch at 11, nap from 11:30-1:00, and you kind of wake her up in the car on the way in to work. Or, if you have a later breakfast (say around 9), you can do the nap from 11-12:30 and let her have lunch in the car on the way to work. For a 2 year old, lunch can be a pb&j sandwich, cheese & crackers, grilled cheese, chicken nuggets--any of those served with a fruit and cup of milk.
On the work-side of things, if your daughter is attending the daycare just like any other kid, I think she should follow the same schedule (for the most part). But, at our daycare they are flexible and will accomodate us when we need to. For example, dd has to go to speech therapy on tuesdays from 11:15-12:45 (this cuts into lunch & nap). So, they hold a plate for her and she eats as soon as she gets back, then takes a shorter nap. I do bring a snack for the drive to/from therapy because I figure she'll be hungry.
What happens in the evening? Does the daycare serve dinner to the late kids? I'd think that they would have to serve something more than a snack if they have kids there until 7 or 7:30?!
Finally, if you don't like the teachers in her class, that's a whole other issue. If you have her in that daycare just because you work there, but you don't really like the daycare yourself, that is a problem! Even with a reduced price and the convenience of having her nearby, you get what you pay for--I say. Is there an alternative childcare option (babysitter, other nearby daycare, family, etc)? At this age, kids do need structure, and a comfortable environment--I wouldn't keep my kid in a place where I didn't feel 100% safe & comfortable!
If it's all about the job, have you considered babysitting or offering your services elsewhere? Of course, you need to look into your state requirements, or just talk to friends and neighbors who might need the help. Then YOU can be the one to bring structure and security to your kid (and others)!