maybe start with SA YD 240:
nor refute his words nor contradict his words in his presence, even to say ‘Father’s words appear to be,’ nor call him by his name, neither in life nor in death, but rather say ‘Father, my teacher.’
RamaH – not even support Father’s position [possibly, without proof, or better to argue with someone who argues with the Father]
Beer Hatev
סותר. בין שחולק עליו בין שאומר להחולק עליו נראין דבריך הוי סותר את דבריו ונראה דסותר את דבריו אסור אפי’ שלא בפניו עכ”ל הש”ך:
Be’er Sheva (Sanhedrin 110a) it is permissible to disagree with a parent, but it must be done in a respectful manner. Not contradicting a parent means, one should not say, “Father, you are wrong.” Rather, one must always speak to a parent in a respectful manner.
Prisha (YD 240:3) it is only forbidden to contradict a parent if one does not have proof. You should not argue with your father just because you feel that he is wrong. But if there is definite proof that a mistake was made in religious matters, then one is obligated to point this out
Chayei Adam (67:8)
Aruch HaShulchan (Yoreh Dei’ah 240:13)
P’sakim U’T’shuvos (240:7) cites the ruling of the Chazon Ish and the Sheivet HaLevi that a child can argue with a parent as long as the child raises his objection as a “suggestion” or “possible thought” and not as an outright objection or disagreement. Likewise, the Aruch HaShulchan (ibid) writes that if a parent asks a child for his opinion, the child may disagree with the parent, even to the parent’s face and even a complete disagreement.