Boy, this would certainly make me angry, too.  Some questions that come
up for me are:
1.  Are they afraid of "catching" something from your milk?
2.  Is Timothy adept at drinking from a cup?  Is it a sippy cup or opened
cup?  Does he make messes everyday?
3.  Is the bottle just easier for them because they can prop it or hand
it to him and go?
4.  Do they understand that bottle nipples are what breastfeeding moms
avoid to prevent nipple confusion?
5.  How would this "new rule" stand up against the state laws protecting
the right to breastfeed because it is clearly the best food source for
the baby and giving it a bottle could interfere with the baby's future
ability to nurse well?  (I would try this route)

Next, you have to consider the implications of causing a ruckus at the
daycare place, if they don't like you, how will they treat your child?
Would you even want to stay with a daycare that is clearly going to act
against your wishes and cause you some potential greif, can you switch?
Can you file a complaint with the Consumer Protection Agency, etc?  Can
you talk to other mom's and see if you are the only one who breastfeeds?
This is very interesting and I hope you let us know what the outcome is.
Thanks for sharing.  Good Luck.
Love Tanya