I see there is a write up about the Carter family and Grace at: http://www.rootsweb.com/~nma/fhbrag.htmhttp://www.rootsweb.com/~nma/fhbrag.htm You didn't say in your post where she was in 1910 so just for others here it is.
1910 Foard Co., TX Census Carter John head m w 56 m1 35yrs TX " Bettie wife f w 50 m1 35yrs 10kids 9living TX " John Jr. son m w 12 sgl TX " Grace dau f w 10 s TX " Herest? son m w 8 sgl TX
I went thru the entire 1910 Texas Census looking for a 'Jack' as a child but to now avail.There were a few 'John's and 'James' but....
I did find a older Jack but I don't think he would be yours.I think about the best thing to look for is his grave.I am also wondering if he might might have been in WWI.It seems as if he died so young that there probably isn't much of a paper trail.
Your situation is much like mine.I can't get past my mother's mother side.It's just a dead end I'll probably never know about.
The older Jack 1910 Bowie Co., TX Census Downey Jack lodger m w 35 s US US US merchant Lodger with Beck Edwin L 42 LA and Lula E 36 AR TN LA
Something Else : Cottle county adjoins Foard county.
1910 Cottle Co., TX Census ED 66 Sh 12B 16 May Downey Robert L head m w 35 m1 14yrs AL US US laborer odd jobs " Leana M wife f w 32 m1 14yrs 4kids 4living AR AR MO " Ralph A son m w 13 sgl OK AL AR " William M son m w 11 sgl OK AL AR " Bertha D dau f w 7 sgl OK AL AR " Ja D P son m w sgl XX NM AL AR***** XX= It appears that the original age was 14 but was marked thru and I can't read the new age.I looked this family up in the 1900 OK census and this Ja wasn't listed so it's probably a younger child of Roberts.