Should the questioner remain with her siblings and take care of them, or is it permissible for her to move in with her father, complete her studies, and show him filial piety, knowing that her father does not care much for her siblings, and her mother wishes for her to stay with them?

If the father needs the son to be with him so that he does not suffer loss, then it is obligatory for the son to stay with him and not obey his mother in preventing him, while checking on his siblings to the best of his ability. However, if leaving the father does not cause him loss, then the son must obey his mother in staying with his siblings, while continuously honoring his father, visiting him, and being good to him.