Did the daycare discuss separating them with you prior to moving them?
I know our girls will often do different tasks to one another while at day care, but they will both still look for one another and are free to go to one another when they need/want to. I think 3 is too young to separate on a longer term basis. Our girls will sometimes go to day care without the other for various reasons, they also have play dates without the other sporadically. But on a regular basis they are kept together. The days that they are together but on different activities, they do so much better, and cope so much better than when they are separated. We wouldn't look at separating them permanently until school age at least.