On 1860 Falls Co, TX census E.R. is on the previous page to my ancestor James Rice and his bro-in-law Henry Standifer.So I am a little familiar with the area.First two Thompson children may have been born in what today is Bell Co., but that county wasn't formed until 1853.
In 1850 Milam County covered many of the counties of today, including Bell and Falls (and Hamilton where Rice & Standifer previously resided.They helped form Hamilton Co, in 1858, moved to Falls by 1860 and then returned to stay in Hamilton before 1870.)
I see in 1860E.R., wife and children are living with Charles Williams, I assume her father.On the 1850 census for Milam there is no E.R., no Thompson born in AR and noneold enough to be his parent.Nor, is Charles Williams there in 1850.From age and birth locations of children for Charles he should be in TX somewhere on that 1850 census.Maybe you can look for TX 1850 counties that have both Thompson and Williams families.
On 1850 census Milam Co, TX there is a Marion Williams b LA, age 20.Maybe a son of Charles and was first of the family to move to the area.