What part of the children’s mission was successful and what part failed (331 -335)?

Even though Jacob, Emma and some of the other students break Miss Peregrine's rules, they discover that they were, in fact, the result of attacks by a wight who, in turn, attempts to have them killed by a hollowgast. The group, however, escapes, evading the hollowgast's pursuit. Jacob faces it alone and kills it, but a short time later discovers, along with the others in his group, that Miss Peregrine has been kidnapped by the wight. Jacob and Emma lead a rescue effort, killing the wight and rescuing Miss Peregrine. Meanwhile, something has gone wrong with Miss Peregrine's time loop, and time in the past is moving forward at its regular rate. Jacob decides to stay in the past with Emma and his new friends, searching out both new loops in which to hide and doing what they can to help others like them fight off wights and hollowgasts.

Jacob's inability to gain his father's understanding is a failure, but the fact that he moves on cements his individuality and illustrates his bravery. In Mrs. Peregrine's words, Jacob is very like his grandfather.