Assalamualikum, I wanted to ask that if my father forbids me from doing that is permissible, but my mother permits me to do the permissible action, will I be sinful for doing the permissible action.
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The criterion regarding obedience to your father is when he realizes a benefit from his command or prohibition, or that there is harm on him in case you do not do a given matter.
Hence, whatever is in this context, it is an obligation to obey the parents in what they order or forbid you from doing even if the other parent has permitted you to do otherwise.
Therefore, if your father had any benefit in what he forbade you from doing, or that he will be harmed if you do such a matter, then you should refrain from doing it as a way of being dutiful to him, even if your mother has permitted you to do it. Otherwise, it is permissible for you to do it whether or not your mother gave you permission.
Nonetheless, it is better for you to convince him and please him as a way of comforting his heart and reassuring him.
Allah Knows best.
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