Hello cupcakes 
Well, confession time, bear in mind that my only child so far is actually minus 4 months old at the moment (do I qualify for mumsnet yet?!), though our house is usually overrun with kids of various ages due to family's/neighbours/friends' offspring coming over... But for what it's worth here are a few things from my experience and my friend who also has a lab and 2 children of her own:
Teach the children as much as you train the dog - e.g. with a puppy that jumps up and nips at clothing, tell the kids to stand up straight and still with their arms crossed and maybe turn their back on pup, don't give the pup eye contact as what he wants is attention. They need to be really consistent and only give attention when he has 4 paws on the floor - calmly praise when he does. Sometimes if the pup gets too excited around them he will need to be taken out of the room for a 'time out' till he calms down. This way he'll gradually learn that he only gets to stay around the family while he's behaving.
Involve the children in training - I've found they get a big kick out of teaching dogs things - silly tricks as well as basic obedience, and it teaches the dog to respect them. All training to be done positively with rewards (whether toys or treats or just praise). A good book is Pam Dennison's "Complete Idiot's Guide to Positive Dog Training". Clicker training is excellent too - Peggy Tillman's 'Clicking with Your Dog' has plenty of things to teach.
Never leave young children alone with the dog - can be hard to do in daily life but I think really important, as even the nicest child gets curious once in a while and decides to find out how hard they can poke... what happens when I stick this in his ear... etc. The dog needs to be protected from any unpleasant experiences with children.
If ever the dog's worried by anything (shouting/screaming/running/playing etc), whatever you do DON'T reassure him as this will just confirm in his mind that there is something to worry about; he will take a lot of his cues from your mood. Instead keep the lead loose if he's on lead (keeping the lead tight is a big signal that you're anxious), put on a bored/upbeat voice and distract him with something he likes (probably food, being a lab ), get him into a sit and to focus on you before giving the treat.
Teach a really solid 'leave' - e.g. leave that kid's ice-cream alone, leave that kid alone completely and come here, leave that dead bird... A good description of how to do it is here: \link{http://www.dragonflyllama.com/%20DOGS/Levels/LevelBehaviours/TL26Zen.html\training website}
She refers to using a clicker, but if you don't have one or want to use one you can use a word like 'yes' instead.
Never allow the children to approach the dog when it's asleep in bed.
Teach the dog that people, including children, coming near his food bowl are not a threat. Don't make the mistake of trying to teach him that you're in charge by taking his food bowl away while he's eating - that only gives the dog a complex and may well cause food guarding. If he shows no signs of food aggression at the moment, drop an extra tasty bit of food in while he's eating - so he learns that good things come from you. Once he's used to you doing that, get the kids to do it too. (Don't do this if he already has issues with food guarding - needs to be done slightly differently).
All these things are just normal training really but I've found them particularly helpful around children as they are all about teaching the dog self-control around little people who are unpredictable and not always very self-controlled themselves.