In what situations in The Art of Racing in the Rain is the quote below true and not true? “That which we manifest is before us; we are the creators of our own destiny. Be it through intention or ignorance, our successes and our failures have been brought on by none other than ourselves” (43).

There are a few events in the book that emphasize the values inherent in the quote above.
Possibly the best example pertains to the havoc Annika causes in Denny's life through her false rape accusation. On a winter trip to Methow Valley, Enzo worries that no good will come from Annika's disturbing infatuation with Denny. Note Enzo's thoughts about this:

Denny was ignorant of her advances; I don't know if it was deliberate or not, but he certainly acted as if he hadn't a clue.

Enzo clearly defines his fears when Denny lets Annika stay at his home for the night. Annika makes sexual overtures to an exhausted Denny, but he repels the fifteen-year-old temptress resolutely. Frustrated by his rejection, Annika eventually accuses Denny of molesting her. So, be it "through intention or ignorance," the narrator proclaims that we are ultimately the master of our own fates. Yet, Enzo extrapolates that the "true hero is flawed."

The true test of a champion is not whether he can triumph, but whether he can overcome obstacles -preferably of his own making-in order to triumph.

Enzo makes allowances for human fallibility and hypothesizes that the true hero can overcome failures that result from his own ignorance or intentions. He believes that Denny could have avoided his predicament but instead, chose to "test his mettle" in a battle of his own making. So, while Annika's false rape accusation sets off a chain of events that lead to Denny being temporarily incarcerated and losing custody of Zoe, it is ultimately Denny's perseverance and steadfast character that saves him from self-destructing.
Because of his exemplary lifestyle, Denny eventually wins visitation rights. He is able to see Zoe and to reassure her that he is doing everything he can to make sure that they will be a family again. Denny's actions reaffirm Enzo's "faith in the balance of the universe." In a supervised meeting with Annika, Denny pleads his case and asks Annika to consider the ramifications of her fury. During the exchange, Denny is compassionate, eloquent, and considerate. He reassures Annika that his rejection was in no way a repudiation of her person.
In the end, Annika drops her false rape accusation against Denny. Because of his actions, Denny emerges victorious; his tenacity obliterates the previous difficulties that were caused by his own "intention or ignorance."
As for any examples that nullify your quote, consider exploring the themes of death and reincarnation in the book. Essentially, no matter what we do, none of us can escape death. Eve dies despite her doctor's care, and Enzo's death shows that living beings are helpless in the face of organic decay. Yet, events in the epilogue suggest that reincarnation, if attainable, is one way human beings can transcend death. However, remember that reincarnation is beyond human intervention or ignorance; thus it nullifies the values inherent in the quote you provided above.