It really depends on how close to your home, or how close to your children, it might be. If you have a bobcat coming up onto your back patio and looking in the house through the glass door, I'd probably be doing something about it, regardless of the threat to my kids. If you're hearing bobcats yowling out in the woods a couple hundred yards out in your backyard, I probably would call the kids to listen, because I still have enough whimsy to think that's cool to hear, but I wouldn't worry.
I'd generally say no, a bobcat won't attack a human. They're typically very timid, and by nature, pretty lazy. They don't tend to go after game that poses a challenge, and limit their work to prey smaller than themselves. I've HEARD a lot of stories about bobcats tearing down deer (HEARD of both fawns and adults), but I've yet to see it. Sure, they'll scavenge on a dead one, but I'm not sure I've ever seen evidence that one attacked a deer.
Picturing a 5yr old kid playing in the sandbox near the edge of the "woods behind the house", I just don't see a bobcat jumping on them as prey.
BUT, I'd definitely put in a few caveat's...
1st: There's a first time for everything. I'd actually say it's probably not the 1st time, but I would say it's incredibly rare if it HAS happened.
Toddlers are a different story. A crying toddler on a patio while you step in to grab a phone might be tempting enough. Plus even a curious bite can be devastating to someone so young. Still highly unlikely, but I just wouldn't risk it.
Cornered cats are an entirely different ballgame. Over the years, we've had a few instances where we've accidentally cornered a bobcat in our outbuildings. I was a few steps behind my father years ago walking into our grainery (narrow alley between a haystack and the grain bunks) and a bobcat came over the top of him like greased lightning. Clawed the heck out of him unintentionally while climbing him like a tree. Happened so fast that I needed a change of shorts, and I was the one in BACK! The old man needed a change of BOOTS!!!
My sister also had one bite the heck out of her hand once when she was reaching up for something off the top of some cabinets in the barn once. She didn't know it was hiding up there, so when she blindly reached up on top, it wasn't playing games.
So, yeah, if it's coming in close contact, I'd put out a live trap, or make an effort to hunt it (I believe in destroying wild animals that have become accustomed to human contact. If you take them out into the country, they're just going to become someone else's problem at their country home, if it's coming into barns or in close contact, even live trapped, I'd shoot it). If you're in a country home and just happen to have a bobcat in the area, I wouldn't worry about it.