To quote from one of my favorite sites,
http://www.catholic.com/tracts/who-c...eive-communion
"The Church sets out specific guidelines regarding how we should prepare ourselves to receive the Lord’s body and blood in Communion. To receive Communion worthily, you must be in a state of grace, have made a good confession since your last mortal sin, believe in transubstantiation, observe the Eucharistic fast, and, finally, not be under an ecclesiastical censure such as excommunication. "
It sounds as if the daughter was not qualified to receive. If she was raised Catholic she should have known that. That said, I think the priest should have simply delivered a blessing and gone on without making a scene.
As to why most other Christians are not able to take RC communion:
"Scripture is clear that partaking of the Eucharist is among the highest signs of Christian unity: "Because there is one bread, we who are many are one body, for we all partake of the one bread" (1 Cor. 10:17). For this reason, it is normally impossible for non-Catholic Christians to receive Holy Communion, for to do so would be to proclaim a unity to exist that, regrettably, does not.
Another reason that many non-Catholics may not ordinarily receive Communion is for their own protection, since many reject the doctrine of the Real Presence of Christ in the Eucharist. Scripture warns that it is very dangerous for one not believing in the Real Presence to receive Communion: "For any one who eats and drinks without discerning the body eats and drinks judgment upon himself. That is why many of you are weak and ill, and some have died" (1 Cor. 11:29–30).