We keep quarrelling about how to raise the children. How can we find a middle way?

Agree on a few core principles in private, then present a united front to the children; different styles can complement each other if they are not turned into a contest.
The Quran describes decisions about a child being made with the parents' mutual consent and consultation (al-Baqarah 2:233), and every parent is a guardian who will be questioned (Sahih al-Bukhari 893). Practical steps: list what really matters (prayer, safety, manners, screens) and agree the rules; leave small things to each one's style; do not overrule your spouse in front of the children; and discuss difficult cases after the children are asleep. Children quickly learn to "go to the softer parent" if parents disagree. If the differences are very large, take a parenting course together or see a family counsellor. See Educating the family.