though there are some dogs that don't shed (or shed very little), there aren't many that satisfy all your needs. off the top of my head, the only non-shedders i know are either hairless or sighthounds or "needy small dogs" lol. but sighthounds are fragile and not suitable for small children who may play too rough.
i suggest you research gun dogs. several of them are good with families and high energy, but quite trainable and able to live in the house as well. also, they're big and strong enough to withstand your children, but family friendly enough to not retaliate and bite them. you being home all day would also keep them happy as they prefer to be nearby you.
if you get over the shedding thing, i definitely suggest a border collie. they mostly only shed during the summer, which we fixed by just going to petsmart to have her shaved every summer. the fur is back by wintertime. they're good indoor dogs and quickly learn any and all house rules including boundaries on certain rooms and such and they're perfect for kids. to this day (and i'm 18 now), i'm pretty sure my border collie raised me more than my mother did (and this is a good thing lol). literally though, she was super-protective. my mother could put me and the dog outside and tell her not to let me leave the yard. if i tried, she stood in front of me or grabbed my shirt and hauled me back to the middle of the yard. to a border collie, children and sheep are pretty much the same thing: objects to be herded. she was also really smart, housebroken in maybe a week, learned every trick the first or second day we tried it with her, and smart enough not to do anything stupid. she would run away to explore and we didn't mind because she actually checked the street for cars (you think i'm crazy, but i've seen her do it). all puppies are overly excitable until they turn maybe two, just so you're aware, but as far as the excitement, my border usually jogs up to greet any new people, lets them pet her head once or twice, and then goes back to patrol the yard.
in all honesty though, for most breeds, i would wait until your kids are older than 4 before you get a dog. if you're at home that you're absolutely sure you can prevent any mishaps, than maybe, but i can just imagine a child leaping from a couch arm onto a dog's back trying to play cowboy or something and now you've got at the very least, a broken leg to pay for and unless the dog is very well-trained (and i woudn't blame the dog) a kid needing stitches from a dog bite.
try a dog breed selector quiz (there's one on animal planet.com.)
subscribe to a dog magazine for tips.
go to your local shelter and look around. take a few for a walk and see what you think.