English Translation
He will drive home, though he is drunk.
The Japanese-English pair doesn’t match.
～と言って聞かない means “he is so stubborn that he cannot listen to other’s reasonable advice/instruction”.
In other words, the English sentence is missing the meaning of “someone failed in persuading him not to drive”.
Also, いってきかない should be written in Kanji: 言って聞かない.