Mom tried tenaciously to convince me(stop my foolishness), but in the end she was the one who gave up.
Reading this at first, i would have read it literally as "mom got caught in my persuasion" or "she got convinced". But with this sentence structure with the ～が、最後に... construction, that wouldn't make sense with two agreeing ideas in a row. So i looked up the expression.
compared to other ～にかかる expressions i can recall:
Why does 説得にかかる end up interpreted in the active voice while the others are in the more intuitive passive voice?