If you haven't entered college yet, the best thing I can tell you to do is to go to a small liberal arts college if you can possibly afford to do so. Lots of the small liberal arts schools offer enough financial aid that they end up being cheaper than state school in the long run, so don't just compare tuition prices--the smaller schools tend to have more financial aid per student than state schools. And they have more flexibility about to whom they're allowed to give financial aid, whereas state schools just follow a strict set of rules.
No matter where you go to school, I can just about guarantee that you are going to have to take what the school will call "general education requirements" or "liberal education requirements." If your parents went to a trade school, they may have a hard time understanding the concept, but basically you have to take classes that have nothing to do with your major, on the general principle that it's good for you to have a well-rounded education. And it's true. You will find, especially if you get into science general education courses your freshman year, that you will be very interested in all sorts of things you didn't previously find interesting, and that some things you thought were interesting at first are in fact quite boring.
The thing about vet school is that you do have to take a certain amount of biology and chemistry, and those courses tend to run in a very specific sequence: it takes 3-4 years in order to complete the sequence. The other thing about vet school is that it's very VERY competitive, much more so than medical school. You need straight As in everything, plus summers spent volunteering on farms to work with large animals, volunteering at the SPCA, etc.
The benefit of a small liberal arts school is that they will be able to shepherd you into those types of volunteer and research opportunities, and you'll have lots of small classes where your professors know you personally--they will be able to write very good recommendation letters for you. In state school, no one cares, and it's up to you to find out all that stuff. Your recommendation letters will be more like, "DuckCrew was in my class and got an A. She seems like a nice person and loves animals." Compared to three pages of, "DuckCrew is the most dedicated and brilliant student I've had in twenty years of teaching, and her work on the molecular differences between BalbC and Black6 mouse immunology in my lab has been critical to the field of blah blah blah," the smaller school is clearly the better choice for getting into grad school.
Also, after taking general education courses, you may well find that you don't want to be either a vet or a lawyer. You don't have to decide for some time. I will say that I know many ex-lawyers who were quite unhappy AND broke all the time, who ended up becoming teachers of some sort: one high school teacher for at-risk students, a community college Civics teacher, a special education teacher. I think the wealthy lawyers were pretty much already wealthy from their parents, and that "startup" money enabled them to start their own practice when they graduated. I know a few reasonably happy corporate lawyers, but they aren't wealthy per se, more like "not starving and sorta comfortable in the suburbs." And ironically, some of them have undergrad degrees in animal health, agriculture, etc. but then went to law school afterwards to become intellectual property lawyers for science-based industry.
Bear in mind that the only reason to decide would be if scholarship money rides on it. AFAIK, the only programs that require dedication and immediate decision-making are the six-year MD programs, if you wanted to be a doctor. Everything else, you can choose to do whenever you like and when it's convenient for you financially.
One last bit of advice: Although your parents may be paying for school, they are going to have to reconcile themselves with the fact that they may not get what they want out of you regardless. My mother wanted an artsy writer/photographer/teacher for a daughter, and she got a biotech scientist instead. Even though my job is curing cancer (among other horrible diseases), and I make decent money, she is still unhappy about that state of affairs because it isn't what she wanted. It's your life to live, not your parents'.
