Sorry, I don't recognize your weed. But I would like to comment on Round-Up and 2,4-D.
1.) Round-Up will kill grass if mixed strong enough. The bane of my existence is buttercups. I had some really bad patches on the edges of our lawn; I used concentrated glyphosate (round-up) and only diluted it by about half the label directions. Then I sprayed the heck out of the thickest areas of buttercups. ...really soaked them. Everything died: buttercups, grass, etc. I had some huge dead patches. I rinsed liberally and re-planted lawn grass. I nursed the grass seeds, but they just never sprouted well. That was last year. This year, all of these areas are now infested with buttercups again. ...and not one blade of grass.
I'm not a fan of round-up. For the cost (even now, with it being available as a generic) it doesn't work like the TV commercials. The first place I tested it was on our long gravel driveway; at best (in addition to only working on broadleaf weeds) it only knocked down the "easy" weeds. Anything with a deep taproot just regrew. And even the shallow rooted, broadleaf weeds regrew within 3 months or so. I just don't think it's cost-effective.
2.) I agree with Marsha Cassada's concerns about 2,4-D. The other problem we have here are blackberries. So I spent an inordinate amount of time researching 2,4-D, agent orange, dioxins, etc. It is challenging sifting through any information out there, because of the "agent orange" slant. I'm not a chemist, but I think some of that is "shock value" from the "anti-everything" crowd. But as a lay-person, I really don't feel comfortable (after reading about longevity, puzzling over the difference between 2,4-D vice 2,4-DT, etc.) where I would let a horse anywhere near anything that had 2,4-D on it. On a positive note: Baby likes to eat blackberry leaves, so she's doing her part for the cause.