Joan, Goodman may have done it different ways on different occasions. In a live performance posted to https://youtu.be/8QUSQJQml40 he sings,

Ever since the dog got drunk and died, and Momma went to prison,
Why, nothing 'round this farm's been the same.
John, you know, when Mom broke out last Christmas,
She drove that old getaway laundry truck right into a train.

I think John Prine must have been in the wings, otherwise I'm not sure what the "John" in line three is about. Then there's a live performance with John Prine at https://youtu.be/J0J1ISJLRb0 where they sing,

Ever since the day my Momma went to prison,
There's nothin' 'round this farm that's been the same.
You know that when they let her out last Tuesday,
She drove her pickup truck into a train.

So, you may well have heard him do it the way you remember it.