We are not residents of Texas, and I cannot completely answer your questions. However, I do have a daughter who is currently studying in a DVM program, and have some experience that might be relevant.
One issue is that at least in what I have seen the students in a DVM program come from a very wide range of undergraduate universities. Also, quite a few of them have veterinary-related work experience both as undergraduate students and also after getting their bachelor’s before applying to DVM programs.
We live in New England (in the northeast of the USA). There is only one DVM program in New England, which is at Tufts University. It is a very good program. However, it is private and being in-state would help very little in terms of cost of attendance. After she graduated university, our daughter moved west to a different state and established residency there. She then worked in veterinary-related jobs until she reached the age of 25. Then she applied to DVM programs. The result is that she is now paying in-state costs in a very good program. Her work experience almost certainly helped quite a bit in terms of getting multiple acceptances to good programs. Her worked experience also helped her to be sure that she wanted to be a DVM, and wanted to put in the time and effort needed to do this.
My best guess is that as long as you (the parents) live in Illinois, your daughter might need to reach the age of 25 for her to be considered independent of you and therefore eligible for in-state costs at universities in most other states. If she graduates university at age 22, then this would give her plenty of time to establish residency in Texas or elsewhere.
One thing to think about is that DVM programs are expensive. You would be best off to avoid debt for undergrad. If possible saving some college money in the bank or 529 might be a good idea. I will also note that UIUC has a very good DVM program (as does your neighboring state to the north).
I do not think that I would care about the difference in ranking between Texas A&M versus UIUC for their DVM programs. I would care about making sure that I could afford to pay for eight years of university with as little debt as possible. To me UIUC seems like a great place for an in-state student who is interested in veterinary medicine to get their bachelor’s degree.