K., I agree with Rachel. Although it shouldn't be an issue with the 9 month old, your 4 yr-old has grown accustomed to having Mommy with her and this is going to be a big change for her. Take some time to visit the childcare center with her. Tell her you are going to playtime. Stay and let her get to know the teachers and some of the other kids there, maybe have lunch with them. If you can manage two or three days' visits you might want to start with an hour the first trip, 2 or 3 hours the next couple of trips and then, when she is comfortable in the environment, she will be more at ease being dropped off for the day. You might even try a test run and, one day while you are there with her, tell her, "I have to run down to get some gas in the car (or some other excuse that won't make her feel she is missing out on Mommy's excitement) then leave for 15 or 20 minutes or so. It will help give her the message that, when Mommy leaves, she will be back soon.
And remember, don't telegraph any uncertainties to her. She will pick up on your fears. Treat it like a great adventure and she will view it in a positive light as well. Then, when the time comes for you to drop the kids off for the whole day, you should be able to take the baby and the toddler to the door, tell the 4 y/o you have to run an errand and will be right back. Chances are the little miss will be happy to visit with her new friends and you may find yourself feeling a bit melancholy at how easily she let you go!