I used to use Roundup when I lived in NM and never really worried about the trees because there are so few out there. Then I moved Central TX where live oaks are pretty much everywhere. I listen to KBLJ AM talk radio on Saturday mornings and would often hear to substitute garden vinegar with a bit of orange citrus oil mixed in as a substitute for Roundup. I bought some last year but I didn't get the chance to use any until this year. I have to say, vinegar and citrus oil works as well, if not better, than Roundup, for clearing up that grass and the weeds that grow in the cracks in the sidewalk and driveway. The grass and weeds died almost immediately and so far haven't come back. I prefer to use a defoliant there because pulling those particular weeds can be difficult and tend to grow back right away if I pull them.
BTW, I never use any weed control products on my yard because of the trees on my property. I've been pulling them the old fashion way with very good results. The grass usually just takes the place of the weeds. The weeds were pretty bad when I moved into my new property 5 years ago but I bought a weed puller that did the job.
FWIW, It's one of these: