A lawyer's duty does not change just because he is appointed rather than hired. A lawyer owes all their clients ethical and zealous representation. You might not like the lawyer that you have appointed to to you or you may love your lawyer it depends on the lawyer not the fact they were appointed.
I think you should view and treat the appointed lawyer the same as if you hired her,
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Your fears are based on a false assumption that an attorney appointed by the Court works FOR the State (or a division of the State). The attorney works for his/her client, and advocates for his/her client. As lawyer's we take this duty very seriously. We are bound by rules of ethics that prohibit the type of favoritism implied by your question. If you are not happy with representation, court appointed or not, you can always ask for or hire someone you do trust. But the fact that someone is appointed should not be the basis for that determination. Good luck.
The answers the other attorneys have given are accurate, but let me point out one more thing you probably haven't thought about and that might ease your kind a bit. CPS cases involve a fairly specialized area of the law, which not many family law attorneys know much about. In my experience, the vast majority (I've never counte or anything, but safely at least 9 out of 10) of CPS litigants do not have the funds to pay for their own attorneys and use those appointed by the courts. What that means, if you think about it, is that your chances of getting an attorney who's familiar with CPS cases and has handled numerous others are actually a whole lot better if you go with the court-appointed attorney than if you sought out a retained attorney. You really don't want to end up hiring someone who normally just handles divorces and private custody cases, but takes on your case on a "How hard can it be to figure out?" basis. Just something to think about.
There are a lot of hard working competent attorneys who are court appointed attorneys. An attorney's loyalty is always to his client and not to the Judge or the county who appointed them, so I would feel very confident that your daughter has an attorney who will be fighting for her rights in a CPS hearing. Your daughter should be forthright with her attorney and she should trust her and judges don't usually appoint attorneys who don't adequately represent their clients. I'm sure whoever is appointed to represent your daughter is a good attorney and one who will work very hard to make sure that your daughter's rights are protected as to her children.