Is my decision to switch from a full-time student to an external student correct or incorrect, especially knowing that my parents do not approve?

Filial piety is among the most emphasized duties and does not diminish with old age. Obedience to parents is obligatory in every matter of good, as long as they do not command a sin or something that causes harm. Based on this, as long as you were certain that your father would not agree to your transfer from regular attendance to external study, you should not have done so unless it was to avert harm. Now, you must review the matter with your father. If he agrees, then all is well. If he does not agree and rectification is possible without harm, then do what pleases him. If rectification is not possible, then apologize to him and convince him of your repentance, promising him not to return to such an act. Go to great lengths to show him affection until he is pleased.