This paragraph is heavily footnoted, as you see. A world-spanning culture is a significant challenge when values of that culture do not line up with the needs of today’s family, said the synod bishops:
84. The Synod Fathers also wished to emphasize that “one of the fundamental challenges facing families today is undoubtedly that of raising children, made all the more difficult and complex by today’s cultural reality and the powerful influence of the media”.(Relatio Synodi 2014, 60)
Baptism begins our influence against cultural trends:
“The Church assumes a valuable role in supporting families, starting with Christian initiation, through welcoming communities”.(Relatio Synodi 2014, 61)
This reference to hospitality is spot on. The media, in order to sell product, caters to those who engage it. Peer pressure or the illusion of it is a powerful force. How do parish communities rise above it? A sincere and welcoming presence from the start.
On rights and responsibilities:
At the same time I feel it important to reiterate that the overall education of children is a “most serious duty” and at the same time a “primary right” of parents.(Canon Law, c. 1136; cf. Code of Canons of the Eastern Churches, 627) This is not just a task or a burden, but an essential and inalienable right that parents are called to defend and of which no one may claim to deprive them. The State offers educational programs in a subsidiary way, supporting the parents in their indeclinable role; parents themselves enjoy the right to choose freely the kind of education – accessible and of good quality – which they wish to give their children in accordance with their convictions. Schools do not replace parents, but complement them. This is a basic principle: “all other participants in the process of education are only able to carry out their responsibilities in the name of the parents, with their consent and, to a certain degree, with their authorization”.(Pontifical Council for the Family, The Truth and Meaning of Human Sexuality (8 December 1995), 2)
I wouldn’t limit the understanding here to an education of facts. It is proper to say children are formed by parents, either by intent or default.
Still, “a rift has opened up between the family and society, between family and the school; the educational pact today has been broken and thus the educational alliance between society and the family is in crisis”.(Catechesis (20 May 2015): L’Osservatore Romano, 21 May 2015, p. 8)
I think this is reasonably accurate. I do think some adults have influence in education, and not always positively. The American indulgence for silliness (evolution and history, to name two) does damage to a new generation. But largely, there is a strain of morality within the American drive for correctness (both ways).
For your reference, remember that Amoris Laetitia is online here.