+1 with blueberry.

At 12 weeks, kittens should not have a trouble with the litter box.

If the kitten is from a breeder, it may be too inbred. If this is the case, then the kitten might not bother to use a litter box.

Another reason why a kitten would not use a litter box is if the kitten was declawed.

yet another reason is if the kitten has a urinary problem. If it has difficulty peeing, or has pain peeing, then the kitten will associate the litter box with pain and will avoid the litter box. This would fall under a medical condition.

Even if there are children around the house, there can be peace between the children and the kittens. Kids need their private space, kitten needs his/her own private space like parents bedroom where it could hide and sleep in peace. Kids can't be expected to play with the kittens anytime they want.
Set up a schedule with the kids to when they are allowed to "harass" the kitten. Other times are scheduled as off limit time. Kitten will learn the schedule just as their feeding time. Feeding time for a kitten should also be scheduled at fixed time. Kitten can be trained to know the feeding time.