it's a little confusing how you wrote that (are we dealing with 3 adults - you, your friend and her adult daughter), but here is what I suggest
go through this IRS tool and play the role of each adult in this situation when you answer the questions. That will explain it to you. will take you under 15 minutes.
where does your daughter live?
https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent
I suspect it will work out that if you are paying more than 50% of the child's support but she doesn't live with you, you can claim her as an "other dependent" (which is the $500 credit). Your friend nor her daughter can because they do not provide 50% of your daughter's support, your daughter is not blood related to them in any way and they are paying less than 50% of her financial support,
if two people claim the same child, the IRS will figure it out.
