My branch of the Alexanders (which includes Vichy from your list) made a number of trips to and from Texas in the 1840's and 50's. They were from the Lauderdale County, Miss. area. My GGrandfather, Isaac Pinkney Alexander, was born in Lauderdale County.There were two reasons for the back and forth. One is that the Alexanders married into the Cherokees often and were contractors to the government to transport Cherokees by wagon from Miss to Okla and Texas. In many cases, they were moving their in-laws.It also seems that they would come to Texas, grow and harvest crops, then return to Miss.Our patriarch was Wesley Alexander, father-in-law to Vichy (a Cherokee) and a veteran of the War of 1812.He died in Houston around 1861.
As far as Caldwell, I don't know.All of the Alexanders in my line settled in Red River, later Franklin County, Texas. Some may have gone on to Caldwell later but it would have been after the Civil War.
Most of those of whom I speak are buried in Clearwater Cem. in south Franklin County.If you have interest in it, Calvin Alexander has written a book on the Alexanders and their migrations to Texas.Full of documentation and photos.