"Hat Schönheit" is theoretically possible, but isn't generally used. It sounds a bit abstract ("has beauty"), you would usually use it in combination with an adjective (like "hat eine besondere Schönheit").
How about "Deine Mutter ist eine Schönheit" instead? "Your mother is a beauty."
To me, "good-lookin'" is a bit different from "beautiful", though - it has a trace of a hint of a sexual connotation for which "ist eine hübsche" might be a more fitting translation.
A couple of other things in your translationtext that I would do differently:
Fische beissen, wenn der Baumwoll aufsteigt.
Fische beissen an (this is specific to biting in a hunting/fishing context)
Using "wenn" is difficult here: it suggests a correlation between fish biting and cotton being high - maybe use "und" like in the original?
"Die Baumwolle" is feminine
I wouldn't use "aufsteigen" to depict a plant's growth. One thing that comes to mind that should work in a gardening/agricultural context is "hoch stehen", as in "Die Baumwolle steht hoch".
"schweigsam" refers to the character trait of being a quiet child. One (but not the only) poetic version of "hush!" would be "Still, mein Kind!"