I'm also a nontraditional student that works a regular 40 hour job. I"m currently getting hours at a research institution affiliated with a large hospital network in our state. Maybe there is something like that near you? I'm lucky enough that my regular job lets me work somewhat odd hours so I work at the research institute twice a week 9-5, and during those days i work my normal job from 5-8am and then 6-8pm, and on the other 3 days i work 10 hour days at my regular job to make up the 40 hours.
Usually whatever school you are taking classes at can help you get research experience. Either by working in a lab at the university or by having some sort of hookup to a research institution like in my case. It might be difficult to balance regular job + research (especially if you are taking classes), but after a bit you can probably dictate your own hours and come in at night or on the weekends.
also, you dont HAVE to have research experience to apply to vet school (unless you want to go into research/get a dvm/phd) as long as you have decent amount vet hours.