If you get a beagle, you must be prepared to take her out for potty breaks- on a leash- every time she has to go, for as long as you live where you live. If beagles pick up on a scent (as Luba mentioned), they'll dash off, oblivious to your calls. Even the best trained beagle on the planet (which I had, but I'm biased lol) will still run off.
The personality of a beagle would be great for you and your kids, but perhaps because you don't have a fenced-in yard, another breed might be better for you. I imagine with four children it won't always be convenient to have to leash up the dog and supervise its potty breaks? You decide.
I do agree that most of the smaller breeds can be quite "nippy".
Labradors are notorious for their tolerant disposition, and make great family dogs. You could also bring your kids to your local shelter, and spend some time with some of the mutts in there, supervised by one of the officers that knows the dog well. Our shelter here has a room inside and an area outside specifically for "visitation" outside of the kennel. Oftentimes, the dog will choose you. See which dog is more interested in your kids than you- that's always a great sign, and they will warm up to you undoubtedly if you take them home!
Best of luck with your search.