the kids had started to barricade themselves away from her and shriek anytime she went near
Your children need the training, not the dog. But not to worry, you weren't to know and are still learning. You can sort this out.
Model correct behaviour with the children. Tell the kids off for screeching. They need to be calm and quiet with the dog.
You didn't know about mouthing and biting, now you do so teach the kids. Don't run away if the dog is snappy, get a toy and play tug or fetch instead.
Physically show the kids that mouthing is harmless. I had to do this with dds friends who get hysterical thinking our dog is biting them. Put your hand in the dogs mouth to show them that it's not trying to hurt you, the dog is not going to bite. This will remove their fear.
(I wouldn't encourage mouthing your hand long term, but physically seeing it happen can help teach the children to understand the difference between mouthing and biting)
Practice with the kids ignoring the dog. The dog doesnt need entertaining at all time. Go about your day - playing with toys, cooking, watching tv, gardening, whatever - with the dog in-toe but not being actively played with Labradors like to just follow you around.
After a while of being part of family life but not over stimulated, for will probably fall asleep. Another lesson for the kids - stay away from a sleeping for. Leave her to sleep.
Then have short bursts of active playing with the dog. Involve he kids in this. For the rest of the time just "be" with the dog.
One practical tip: leggings or shirts are better than flappy trousers (which puppies like to hang off).