As a way of life, Islam has determined specific right and duties for every element of the family. There are fair rights as well as duties upon everyone without infringing the rights or duties of the other. Parents have rights towards their children and similarly children are asked for duties related to their parents. In the same time, the whole family has rights towards the society they live in and they owe the society equal rights for them.
Islam made it a responsibility upon everyone that they will be asked for on the Day of Judgment and will endure Allah’s displeasure and punishment if he or she fails to undertake them.
The rights of children in Islam are numerous, including choosing a good righteous mother (i.e. wife who will be a mother of your children) and proper name, ensuring them a respectful life, dealing with them in a good way, ensuring them proper upbringing and education, and other many rights we can know from this interesting video by Sheikh Yusuf Estes. Feel free to watch this video that talks about the status and rights of children from the Islamic point of view.