There are 2 Henry Padgett's listed in Texas in the 1920 head-of-household index.Neither is close to Dimmit County, but here they are anyway.The census date for 1920 is 1 Jan 1920
1920 Texas, Robertson County, ED 180, Sheet 12A
Henry Padgett, Head, 21, born in Texas, parents born US, Farmer
Belle, Wife, 21, born in Texas, parents born Alabama
Herman, Son, 1 month, born in Texas
1920 Texas, Brazos County, ED 11, Sheet B
Henry D. Padgett, Head, 44, he and parents born Alabama, Farmer
Dora, Wife, 39, born tx, father born Texas, mother born Mississippi
Claude, Son, 19, born Tx
Dora, Daughter, 17, born Tx
There is also an H. Padgett, a boarder in Dallas:
1920 Texas, Dallas County, ED 87, page 2B
R.R. Robertson, Head, 56
Martha E., Wife, 49
Robt, Son 21
B P Esty?, Boarder, 46
H. Padgett, Board, 29 (divorced), he and parents born South Carolina, laborer at a cotton line?
Ed Jack, Boarder, 50 (married)
Janis Lee Jack, Boarder, 48 (married)
It appears that the boarders worked for R.R. Robertson.All of the boarders were laborers at a cotton ??, and Robertson was listed as Cotton Manager who owned his own business.
I searched all of the counties directly adjoining Dimmit and didn't find any Padgetts in any of them (and I used Soundex).
I searched for McCarleys in Dimmit County in 1920 and found 4 -- none of them had a daughter named Carrie living with them, nor did they have a daughter aged about 21 (you said that Carrie was born about 1899).I did a reverse search and looked for men named Henry in Dimmit County in 1920 (just in case the last name was transcribed incorrectly), but none of the ones in the index were the right one.
This is frustrating!!!I wish I could be of more help.