My daughter attends Southwestern in Georgetown, and it also claims to be the oldest college in Texas. The operative words here may be "continuously operating". SWU has quite a colorful history. She's home for the weekend and when I mentioned your post she demanded I defend her university's honor, lol. By the way, she visited Austin twice during her college search (along with Trinity and Southwestern), and it is a wonderful school. Your daughters are proof of that.
Baylor was originally chartered in 1845, but didn't confer their first degree until 1854. In 1886 they consolidated with Waco College, which was under control of a different Baptist group beginning in 1847, and a new charter was issued as Baylor University at Waco (The original Baylor had been at Independence) in 1886.
So, Southwestern has the oldest roots, Baylor's roots go back farther than Austin College's, but Austin College has been operating under the same charter the longest, in fact since it's original founding.
The site in Huntsville where they were originally located is now the site of Sam Houston State, having passed through the hands of a short lived Methodist school. When the last remaining former Austin College building burned down some years ago, some of the timbers were salvaged and a ceremonial "Mace" constructed of one of them was presented to Austin College by Sam Houston (or it's students). That Mace leads the procession at Graduation and other important events at AC, along with 2 to 4 pipers in keeping with the school's Presbyterian roots. It's an impressive beastie. :)