Here is the sentence again:
The comma between peach and because causes a comma splice. At this spot, there are two complete sentences joined with just a comma, which is too wimpy a punctuation mark to do the job. Jean always nibbles around the pit ... begins the first complete sentence. Because she is vain about her smile, she doesn't want ... starts the next complete sentence.
To fix this problem, you could put a period after peach and capitalize the B for because.