What's the best way to stop my 22-month-old from attacking the other kids at day care?
The fact that this is happening where she's receiving child care tells me that this isn't something you can do on your own. You'll need to coordinate your efforts with your daughter's child care provider. That way she's getting the same message from two important sources and knows that the rules apply in both places.
As for changing the behavior, you're best off taking a three-pronged approach. First, help your child identify what she's feeling when she's upset. ("I can see you're angry that we have to stop playing.") That gives her some words to describe her emotions. Second, use a simple rule, such as "People are not for hitting. We don't hit people." Third, show her a more appropriate way of expressing her anger. This might be stomping her feet or punching a pillow.
As she grows older and more verbally skilled, she'll learn to use words to let people know when she's upset.