Re: Can a child receive the precious blood?
First, a correction of verbs may be helpful in shaping a better understanding in your daughter of her attitude toward Communion. Encourage her to stop thinking that she is "taking" Communion; instead I urge you to inculcate in her the habit of understanding that she is "receiving" Communion. It may well help her to understand that Communion is a gift and not an entitlement.
Second, although I have not heard of the idea of "carding" communicants at Mass, and would be surprised to hear of a 19- or 20-year-old being turned away from receiving the precious blood, I am not surprised that some parishes are hesitant to offer the precious blood to young children. Even older children can have accidents that cause spillage of the precious blood. (You'd be surprised how often we hear from parents asking how to launder children's clothes that have been stained with the precious blood.) Rather than telling a child your daughter's age that there is fear she might spill the precious blood, some might consider it more respectful of her dignity to tell her that there is an age requirement for receiving from the chalice.
Third, there is no absolute requirement that communicants must be offered the chalice. For centuries the Church restricted all laity to receiving the host alone. If your daughter is upset at the idea that she did not get to make a "full Communion," then she needs to be taught that Christ is fully present under both the consecrated host and the consecrated wine, and that a "full Communion" is made by receiving one or the other. It is not necessary for a layperson to receive both.
Finally, even if the parish your daughter attended may not be fully correct in its understanding of whether or not a child should be given the precious blood (and I suspect that there has been some misunderstanding), I encourage you to require your daughter to respect and follow the instructions of those in authority over her, even when they are not entirely correct, so long as what they require is not itself sinful. It seems to me to be a more important lesson for children to learn that insisting on personal rights is not always the highest value. Sometimes it is more important to humbly obey from love of God, even when someone in authority is requiring something of you that is not completely just. After all, that is a lesson you may need to draw upon yourself in your own relationship with your child.