Back when I was in college 3+ decades ago, qualifying for in-state tuition wasn’t very difficult. I didn’t know anyone who paid out of state tuition for more than a year. But now from what I have read, its much more difficult in most states to do that. Will vary by state so you should check specific state requirements. But often it is triggered on why you came to the state. If you came for education, you cannot qualify for in-state tuition. Everyone I know who went out of state for undergrad paid out of state tuition for 4 (and a couple more than 4) years. But I don’t think that is universally true.
In terms of feeder programs for vet school, I am not sure there are many of those (and definitely not when you look at the schools themselves). Vet schools tend to be large state schools with large numbers of undergrads and large animal science undergrad programs. As a result, they have a lot of applicants to vet schools and as a result get more admissions than do smaller schools with fewer applicants.
At one point, the convention wisdom was you only needed to apply to the vet school in the state of your residence because if you didn’t get into that school, its unlikely you would get in anywhere out of state. I think that is somewhat less true today (depending on the school). In/out of state percentages vary by school (3 where my daugther applied vary from NC State at 80% NC residents, Wisconsin at 66% WI residents and Ohio State at 44% Ohio residents).
More than the undergrad you think is a good feeder school, I would look for one at which your kid will best succeed. Grades will be important. Also, as already noted, debt should be avoided for undergrad to the extent possible. Vet related experience will also matter.
I definitely wouldn’t limit the search to one vet school. Different schools are looking for different types of applicants. Not getting into one doesn’t necessarily mean you won’t get into another. Best of luck to your daughter.