With kittens the introduction to other members of the household should be gradual. Children need to let the kitten come to them, rather than just pick it up. Playing stops when the kitten chooses and then it should be allowed to go back to its bed and be undisturbed. Be aware that kittens can scratch and play-bite when they are around young children.
Again with introducing kittens to a dog it needs to be done carefully. An ideal way is to have a mesh pen in which the kitten can sit safely till they become accustomed. Dogs not used to cats should be kept calm and on a lead. This can take sometime, patience and rewarding the dog for behaving well.
With quieter dogs or dogs used to cats, they can be introduced using a strong cat carrier. The dog again should be kept initially on the leader, placing the carrier on a higher surface to allow a controlled introduction. Do not leave the new kitten alone with other cats or dogs until they are well established in the household.