You're spot on about the Farmer Boys. The lyrics don't seem to be on the web but there's a German outfit that seems to be selling the disk here. The record title appears to be

FARMER BOYS

FLASH, CRASH & THUNDER

BCD 15579 30.00 DM
which I assume means that they sell it for thirty deutschemarks.

The other song may have been recorded by Arkie Sibley. Here is a segment from a commentator on some related "HOTROD" songs found here.

Capitol 1633 by Jimmie Dolan is also shown as "Hot Rod Race," but may in
fact actually be "Hot Rod Race #2," although I've not seen anything to
verify that Jimmie Dolan actually recorded the sequel. I do know that he
recorded a song called "Hot Rod Mama" (Capitol 2244), which may be the same
song as by the elusive Gene LaVerne on Western Hit Parade. Anyone with
definitive information on either of these items is asked to contact this
writer. "Hot Rod Mama" is definitely not another version of "Hot Rod Race/
Lincoln."

After Ramblin' Jimmie Dolan covered "Hot Rod Race," Arkie returned the
favor with a cover of Dolan's "Playing Dominoes And Shooting Dice" (or
it may again been the other way around, I've not been able to date the
Shibley version).

But Stomping Tom says otherwise:

Last but not least, are Hank Snow's "The Night I Stole Sammy Morgan's Gin" and "Playing Dominoes and Shooting Dice" (a song originally done by Phil Harriss from the Jack Benny Show and the voice of Baloo from the Jungle Book Movie).

However here at Vintage Countryis where you can buy a recording of the Shibley version listed as ARKIE SHIBLEY Hot Rod Race
Hot Rod Race, Playing Dominoes and Shooting Dice, Guitar Hoedown, etc 25 tracks.

Sorry I was not able to find the words for you, though.