Depends on the breed and kids. Larger breeds mature slowly, sometimes taking upto 3 years to settle. If kids are super active and intice puppy to play roughly with them, run around screaming and etc, even small dogs would remain troublesome around them.
I got a 5 m.old Jack Russel puppy when DD was 2 1/2. Her every squil and hand flailing sent him ito jumping and play biting mode. she wanted to play with him and would pick up his toys and hold them over her head, he would jump on her and knock her down. It took about 3 months of us constantly saying: "DD, keep toys low" "dog, leave it" over and over and teaching DD and puppy how to play well together. It got better after 3 months but I could not safely have my dog with my nephew even after the dog has settled a bit, because my nephew is high energy kid who would trigger all of the puppys instincts and he would grab his hands and chase him.