So back in 1959 all you had to pay for a serious drunken driving offense involving a car accident was two lousy dollars and no other fines or restrictions. Wow.
"'Extremely High Voltage.' Well, I don't need safety gloves, because I'm Homer Simpson--" - Frank Grimes
It's a reference to an old vaudeville sketch. A version of it was filmed for 1945's Ziegfeld Follies, in which Victor Moore is ticketed for spitting in the subway, for which the fine is two dollars, but his lawyer friend Edward Arnold insists he fight it and refuse to pay it.
Moore loses in court and is sentenced to jail time, Arnold appeals to a higher one and the process is repeated several times, with the sentence increased each time and Moore crying to Arnold in desperation, "Pay the two dollars," before he finally finds himself sentenced to death.
So Roger's mother's remark is merely a punchline-like way of saying, "Stop fighting it and pay the fine."
Which is one of the funniest sketches I've ever seen, totally hilarious, with no relief for either Moore or the viewer!
A vaguely similar kind of monetary allusion occurs in the Nancy Drew series, where Nancy regularly says something like "I'll bet you twenty-three eighty that ... ".
Thanks for clearing that up! Just like the OP, my first thought was wow, they're sure lenient on drunk drivers. Not only did he almost hit a bicyclist, but he caused several cars to swerve off the road and it was a stolen car! All that for $2, what a bargain.
So yes, what was the real fine for driving while intoxicated back then?
It's ironic now, cause I'd just gotten ticketed for what is to be a $70 fine. Damn, I wish I lived in the 1950s. Could I get a DeLorean Time Machine? 😝