Dog breed statistics are extremely unreliable. See this magazine's example for an explanation as to why.
We all differ in our experiences. DrNortherner considers Labs bomb-proof. Clearly she hasn't met mine. In Ireland my GSD would be legally viewed a potential danger and on the restricted breeds list. Yet my GSD boy is as good natured as DrNortherner's Lab. I have 2 DDs who help alongside me in a rescue. I've had large breeds, and SBT/SBT X all their lives, both as my own and foster dogs. I've only been bitten twice in 45 years (and one of those occasions was due to my own stupidity, the other by a badly injured, scared dog). My DDs have never been so much as scratched.
So what makes us different?
I do.
I would never have put my (or any) dogs in a situation where a child could hit him. If the child can't be trusted, whether because of age or pure bad behaviour, then keep him away from the dog. My exact words to my DDs have always been (get your flame-throwers out ladies, you won't like this):
"If you get bitten by one of my dogs. don't come to me expecting me to turn on him, because it will most probably be your fault".
I know my dogs, as well as anyone can be expected to. I know they won't bite unless provoked and going by the millions of contented dog owners out there I'd say I'm in the vast majority. And of course it's my responsibility to make sure of that... and I have.
Likewise it's your responsibility to protect your DC AND your dog. It isn't that hard, I managed it as a lone mum who has had dogs since the DDs, with 19 months between them, were born. I would honestly say that you would be premature to get rid of a dog without trying, and you've only had pup a few weeks. And god knows there are enough being killed for want of homes, in their thousands each week, I'm no advocate of rehoming unnecessarily... and I do think it is unnecessary, provided you are willing to make changes to your way of doing things and both teach your DC whilst seperating them whilst they are too young to fully comprehend. If you don't, it would imho be because you won't, in which case Kid is completely right, it is far better to rehome now.
It's in your hands. It is possible. Training classes are a good idea, but you can only train a dog to have a certain behaviour so far. The rest is down to how you behave with him.
For the record, I have only ever used crates with foster dogs - ie unknown quantities or at the request of the rescue concerned and/or owner-to-be. My DDs were left unsupervised with my dogs when small, because I had the measure of both. I'm not advocating this for you, perhaps far from it, but am pointing out that I didn't achieve safe DDs and safe, well behaved dogs by being a helicopter type of parent.
Honestly, it can be done. A Lab pup shouldn't be an excessive risk to any child, you have a blank canvas to work with, not a dog with any established behaviours or issues from the past. On that score I'd say, ime and imho that the risk of harm is very low, in the same way that crossing the road sensibly is, but ONLY if you are willing to prevent your DCs from inciting it.
Perhaps have a word with your breeder and Labrador rescue, or one of the rescue forums such as DogPages for tips and advice to suit your own home/lifestyle/set-up? Don't give up yet!