Jenkins gave Haley two driving lessons off-screen before the episode he appeared in. Those two times, Haley failed, one time driving into the bushes as Alex mentioned, and he yelled at her, causing Haley to think of him as so mean.
In "Fears", Haley was constantly thinking that Jenkins hates her only for Claire to contradict her. Jenkins first appeared when coming out of the drivers building with a driving test clipboard and when Haley sees him, she gets upset and hopes she will not be with him again and passes her. When she thinks he's not with her again, Haley says "Oh, thank God", only to then hear him say "Well, come on. I don't have all day." meaning she is with him again (Oh no!)! Haley says she's gonna throw up, but Claire tells her to get in the car, put on her seatbelt, take three deep breaths and relax and Jenkins then says "Yo. Let's move it, Two Strikes." and Haley sets off with him, scared.
During the test, he tells her to turn left at an intersection, but instead goes right. Jenkins gets furious and shouts a little bit and Haley saying she's trying. Jenkins tells her to pull over, but Haley refuses saying she can do this, but Jenkins shouts "Pull over now!" and when she does, the camera cuts to Haley crying. Jenkins asks why she's crying and Haley asks him why he hates her to which Jenkins replies that he doesn't hate her, that she seems like a nice girl and that she reminds Jenkins of his daughter... which is why he wants Haley to live a long and happy life and be safe, and not hurt his daughter.
Haley said she really wanted her licence and she swore she had been practicing a lot. Jenkins asked her if she would drink and drive or text and drive (separately) and Haley's answer to Jenkins's two questions were "No, sir.". Jenkins decided they should start from the beginning, although Haley asked him if he could smile first because if he smiled, she would be less nervous. And so, he gave Haley a smile, only for Haley to reply "Okay, that didn't help." and Jenkins replies "Just go."
Jenkins's final appearance was when he and Haley returned to the drivers building where Claire and Alex still were and Haley had managed to earn her driver's licence and ran out happily, but nearly lost it when she forgot to put the brake on with Jenkins still inside the car and car was not in park, and so Jenkins puts the brake on instead. Claire tells Haley to run fast to the counter which she does as Jenkins stares after her, but is then staring at Claire and Alex.