Sounds like your daughter and Sarah are mean-girls in training. I do not mean to be harsh, or want to make sweeping judgements, but I say this based on the scenario that you share. I know no one wants to believe their kid is a bully, but really? A "schedule" for who can play with whom? If my kid came to me with that lame story, my "bully-meter" would be buzzing and ringing about now. This IS bullying at it's best because it is a form of isolating and exluding someone from the group by putting unfair conditions on their friendship.
If I were on the receiving end of this story, I would gulp hard and focus on filtering the spin your daughter is giving you about Casey being annoying and that Casey doesn't like to share Sarah etc. Sounds like quite the opposite to me....more like Casey isn't liking this "schedule" solution which is putting conditions and limits on their friendship, and thinks your daughter (and possibly Sarah) are unfair and unkind and is seeking their acceptance and approval.
If she has to ask frequently... "Are you my friend today?" and ..."Why aren't you talking to me today?" ...then it's easy to conclude that your daughter probably hasn't been very kind to her of late. Your daughter may say her questions are annoying, and that Casey isn't giving her space, but could your daughter be trying to justify her treatment of Casey for your benefit by cutting her down and making her out to be this needy geek?
Based on Casey's actions via your daughter's filter, I'm guessing the playtime schedule was NOT Casey's idea, but something your daughter and Sarah made up to control Casey. I don't think Casey is as "geeky" and socially in-ept as you and your daughter seem to think. I think she's reacting normally to what most would consider abusive treatment. No one wants to be rejected or feel rejected. It sounds like somewhere along the line, Casey's feelings have been deeply hurt and she doesn't understand why the friendship has become a cold war. Her mom's FB message supports that guess. While the friendship "schedule" could be enough to make any person act seemingly needy, I'm certain there is more than this going on. To solve and rectify this situation, you need to find out what has been going on and why.
You yourself should be careful to avoid rationalizing your daughter's "hearsay" about Casey by piling on judgements like..."Casey is small for her age and dresses very young...and just acts very immature for her age...etc." I hope you haven't shared your personal judgements and opinions about Casey's appearance, birth order and behavior with your daughter. True or not, they are damning and certainly would influence and reinforce your daughter's feelings and furthermore justify her ill-treatment of Casey away from home.
Furthermore, you're right, you don't have the full story. Since you FB with everyone's mom, you may want to talk face-to-face (not on FB) to Casey and Sarah's moms to get their daughters' side of the story before this turns uglier. And believe me, before the end of the year, it will get uglier if left unchecked. When you talk to their moms, you need to be ready to hear things you might not want to hear about your child. Avoid being reactionary and defensive, but try to work with everyone on finding ways to help the girls to be kind to each other so they can get through the remainder of the school year with some semblence of peace.
Next, talk with your daughter about kindness and tolerance and say it is unfair and shallow to judge people based on their clothes and hair. Explain that Casey may be feeling excluded if this "scheduled" play-time wasn't her idea and that is why her behavior may seem annoying. She just wants reassurance you are still friends.
I know your daughter said that she's worried about Casey getting bullied next year, but it is already happening. Let your daughter know, things like "playtime schedules" are forms of bullying if someone is feeling exluded or is purposely left out because of it. Say they need to get along as a team. If it turns out after talking to your daughter about this exluding stuff she just isn't into Casey as a friend anymore, encourage her to just end the friendship cold-turkey AFTER...not before... school lets out for the summer by not being available anymore, rather than feign friendship only to mistreat the girl.
That isn't to say she should suddenly start ignoring her at school and give the cold shoulder...it .just means she shouldn't make herself available for socializing outside of school in the future. She should be encouraged to always give a friendly smile and say "hi" etc. like she would with anyone at school. Be sure to encourage her to wait until school lets out for summer break. It will be much easier on everyone to distance over the summer months, and by next year they may be in separate classrooms making it easier to break ties without drama and without hurting each other's feelings too much.
If your daughter chooses to end the friendship, be sure to remind her good friends are hard to come by...and shallow friendships are a dime a dozen. Before she decides to sever ties, if that's what she chooses, help her to reflect on what makes a good friend, and how she would feel if this were happening to her or sometime in the future Casey should turn on her in an unexpected way or bully her. After reflection, she may change her tune and decide Casey isn't so bad after all. Who knows?
Sure you could stay out of it as others have mentioned, but I think if you don't nip this now with your daughter, she'll carry this behavior into future relationships in the years to come. This is learned, negative behavior that won't go away. Kids don't outgrow this...it becomes their way of operating in life. If you want to be proactive, get involved. This is what a school counselor would recommend anyway.
Remember, kids bully most of the time because it gives them a sense of power and control, not because their target is necessarily problematic. How could Casey be a friend one minute and the object of avoidance and scorn in the next? Easy if it means you're not on the receiving end of peer pressure and pack mentality.