I def. don’t agree with the kids being whatever the father is, and if you look back this is not always historically the case. A few Arab tribes are matrilineal, with ppl claiming descent through the mother. And anyone who is claiming to be a Syed is doing so on the basis of relationship through Prophet’s daughter, Fatima.
Children are the product of both of their parents, and neither side should be given preference over the other - Ranjhan - you sound like my in-laws.
BTW, if the father’s side should have preference islamically, then the mother would not keep her name after marriage. Even custody favors the mother’s side. If somethings happens to the child’s parents, custody first goes to the mother’s mother, then her sister, and so on, and to the father’s family last.