Is one sinful for missing the Fajr prayer due to caring for his daughter, and is his action considered intentional delay of prayer?

It is permissible to delay the prayer until the end of its time, but this is contrary to what is most preferable and involves a risk. As for being preoccupied with silencing a child when the prayer time is short, to the extent that its time expires, this is forbidden and necessitates repentance, unless the one delaying is certain or has a strong presumption that this will not cause the prayer to be missed within its time. Whoever intentionally leaves the prayer until its time has expired does not become a disbeliever.