What are the parameters for obeying parents if their commands contradict the method of raising children that the father deems compliant with Sharia, such as when they order him to leave his son alone in a certain matter while the father sees the necessity of his intervention?

Obedience to parents is obligatory unless they command a sin, or something that causes harm to the child or those under his care, or something that entails unusual hardship. However, if you disagree with your parents regarding the upbringing of your children, obedience is not obligatory if their command involves a sin, harm, or hardship. You must deal with them gently, speak kindly, and avoid showing disagreement as much as possible. If their command is free from these three impediments, then obedience to them is obligatory, along with striving to be dutiful and kind to them.