Well, as to the breastfeeding side of it, if she'll definitely get milk at lunch she should be ok even if she doesn't drink anything the rest of the day. You'll probably have to make up for it in the evening/night/weekends though. My ds used to nurse for about 3 hours on Saturday mornings!!! Maybe she could drink some water in between times, even if she won't take the milk.
As for the separation, try to make sure that there is one consistent authority figure she associates the daycare (your cousin I guess). I had the same issue with my ds, and he used to scream the whole time I was gone if I left him at home with my dh! I thought he was never going to get used to daycare. But at home, if you leave, for the baby, it feels like Mommy was the person I depend on, and she just left! Anything could happen! But at the daycare, if you are not the person in charge, if you are not the person that everything depends on, then it's ok that you leave. So - you need to get her to perceive that someone else is the Rock of Dependability at daycare, and not you. Then she might be ok. See if you can get the daycare to accommodate this, for example, at the beginning they might make a special effort to have one person stay with her the whole day, instead of switching off like they often do. Later, when she gets used to the space, she can get used to the fact that there are many people who work there.